Q. How should we interpret the expression "enter the holy place by the blood of Jesus"?
A. Platonically.
That is, everything in the Tanach, the intertestamental books, Greco-Roman religion, all rituals of the Tanach, etc. are obviated by Christ, and replaced with an ethic of faith, hope and love. The NT authors spill a great deal of ink to show that the Temple, the Priesthood, the Sanhedrin, the sacrificial system, kosher laws, "Churches," "Holy Days," Passover, Torah observance, and so on are no more (or that they would be no more with the destruction of the Temple). NO rituals. Nothing public. Secret piety, not public piety.
In Hebrews, he's focusing on the obviation of the Temple, Yom Kippur, and some other things. He compares and contrasts the orthopraxy of the Jews with much better things, consisting of faith, hope and love.
According to Hebrews, once per year on Yom Kippur aka "the Day of Atonement," the priest had to make two sacrifices before he could enter the holy place, one for himself and one for the people, but Jesus did them both in one shot:
[Heb 7:27 NKJV] [27] who does not need daily, as those high priests, to offer up sacrifices, first for His own sins and then for the people's, for this He did once for all when He offered up Himself.
[Heb 9:7 NKJV] [7] But into the second part the high priest [went] alone once a year, not without blood, which he offered for himself and [for] the people's sins [committed] in ignorance;
Hebrews seems to make a very clear point that Jesus had a moral failure of cowardice:
[Heb 2:14-18 NKJV] [14] Inasmuch then as the children have partaken of flesh and blood, He Himself likewise shared in the same, that through death He might destroy him who had the power of death, that is, the devil, [15] and release those who through fear of death were all their lifetime subject to bondage. [16] For indeed He does not give aid to angels, but He does give aid to the seed of Abraham. [17] Therefore, in all things He had to be made like [His] brethren, that He might be a merciful and faithful High Priest in things [pertaining] to God, to make propitiation for the sins of the people. [18] For in that He Himself has suffered, being tempted, He is able to aid those who are tempted.
[Heb 5:1-10 NASB20] 1 For every high priest taken from among men is appointed on behalf of people in things pertaining to God, in order to offer both gifts and sacrifices for sins; 2 he can deal gently with the ignorant and misguided, since he himself also is clothed in weakness; 3 and because of it he is obligated to offer [sacrifices] for sins for himself, as well as for the people. 4 And no one takes the honor for himself, but [receives it] when he is called by God, just as Aaron also was. 5 So too Christ did not glorify Himself [in] becoming a high priest, but [it was] He who said to Him, "YOU ARE MY SON, TODAY I HAVE FATHERED YOU"; [6] just as He also says in another [passage,] "YOU ARE A PRIEST FOREVER ACCORDING TO THE ORDER OF MELCHIZEDEK." [7] In the days of His humanity, He offered up both prayers and pleas with loud crying and tears to the One able to save Him from death, and He was heard because of His devout behavior. [8] Although He was a Son, He learned obedience from the things which He suffered. [9] And having been perfected, He became the source of eternal salvation for all those who obey Him, [10] being designated by God as High Priest according to the order of Melchizedek.
Paul also speaks of Christ dying to sin:
[Rom 6:8-11 NASB20] [8] Now if we have died with Christ, we believe that we shall also live with Him, [9] knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him. [10] For the death that He died, He died to sin once for all [time;] but the life that He lives, He lives to God. [11] So you too, consider yourselves to be dead to sin, but alive to God in Christ Jesus.
So if he was ultimately relieved of all of the pain of the execution except the three easiest hours of a process that was designed to last for days, then to whom did God pass the cup that he was supposed to drink? Paul:
[Col 1:24 NKJV] [24] I now rejoice in my sufferings for you, and fill up in my flesh what is lacking in the afflictions of Christ, for the sake of His body, which is the church,
[Act 9:15-16 NKJV] [15] But the Lord said to him, "Go, for he is a chosen vessel of Mine to bear My name before Gentiles, kings, and the children of Israel. [16] "For I will show him how many things he must suffer for My name's sake."
So we can see how relieved Christ was to have a vicar:
[Psa 22:19-25 NASB20] [19] But You, LORD, do not be far away; [You who are] my help, hurry to my assistance. [20] Save my soul from the sword, My only [life] from the power of the dog. [21] Save me from the lion's mouth; From the horns of the wild oxen You answer me. [22] I will proclaim Your name to my brothers; In the midst of the assembly I will praise You. [23] You who fear the LORD, praise Him; All you descendants of Jacob, glorify Him, And stand in awe of Him, all you descendants of Israel. [24] For He has not despised nor scorned the suffering of the afflicted; Nor has He hidden His face from him; But when he cried to Him for help, He heard. [25] From You [comes] my praise in the great assembly; I shall pay my vows before those who fear Him.
So when Jesus tapped/wimped out, Paul took over.
So how could Jesus enter the holy place? Not without blood:
[Heb 9:22-28 NASB20] [22] And almost all things are cleansed with blood, according to the Law, and without the shedding of blood there is no forgiveness. [23] Therefore it was necessary for the copies of the things in the heavens to be cleansed with these things, but the heavenly things themselves with better sacrifices than these. [24] For Christ did not enter a holy place made by hands, a [mere] copy of the true one, but into heaven itself, now to appear in the presence of God for us; [25] nor was it that He would offer Himself often, as the high priest enters the Holy Place year by year with blood that is not his own. [26] Otherwise, He would have needed to suffer often since the foundation of the world; but now once at the consummation of the ages He has been revealed to put away sin by the sacrifice of Himself. [27] And just as it is destined for people to die once, and after this [comes] judgment, [28] so Christ also, having been offered once to bear the sins of many, will appear a second time for salvation without [reference to] sin, to those who eagerly await Him.
Notice that the words "reference to" were added, and corrupt the meaning of the passage.
Notice also that the words "we are, yet" were likewise added, and the preposition for "separate/apart" is rendered as "without." No, no. He is saying that when Jesus would return (c. 70 AD/CE) he would be free from Mr. Sin, and would have learned to obey God.
[Heb 4:15 NASB20] [15] For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things just as [we are, yet] without sin.
So because Christ died to sin and shed his blood for the people also, he was qualified to enter in to the holy place. But how? Technically, what does bloodshed accomplish?
The prevailing interpretation of the meaning of the death of Christ is The Satisfaction Theory:
The satisfaction theory of atonement is a theory in Catholic theology which holds that Jesus Christ redeemed humanity through making satisfaction for humankind's disobedience through his own supererogatory obedience. The theory draws primarily from the works of Anselm of Canterbury, specifically his Cur Deus Homo ("Why was God a man?"). It has been traditionally taught in the Roman Catholic tradition of Western Christianity. Since one of God's characteristics is justice, affronts to that justice must be atoned for.1 It is thus connected with the legal concept of balancing out an injustice.
Or perhaps Substitutionary Atonement theory. But regardless, they are both utterly stupid, stupid, stoooopid. Why? Because they are based on the principle that two wrongs make a right. It suggests that God doesn't care who his wrath falls upon, as long as he gets to vent. I like to compare its "logic" to this:
"You raped my daughter; how about if you kill my son and we'll call it even?"
Would that satisfy the father? I trow not.
It also interprets the death of Christ as an act of justice, or even one of commerce (Christ "paying for sin.") It was decidedly not. It was an act of grace.
The correct interpretation is given by Paul in Romans 3:25, and is called the Governmental Theory.
But Hebrews goes another way. He says that the death of Christ gave "teeth" to the New Covenant. In other words, the New Covenant was a blood covenant that was ratified over the death of God's son, and that New Covenant provided forgiveness, without the activities of the Torah:
[Heb 9:16-17 BBE] [16] Because where there is a testament [IE: covenant], there has to be the death of the man who made it. [17] For a testament [IE: covenant] has effect after death; for what power has it while the man who made it is living?
[Heb 9:11-20 YLT] [11] And Christ being come, chief priest of the coming good things, through the greater and more perfect tabernacle not made with hands -- that is, not of this creation -- [12] neither through blood of goats and calves, but through his own blood, did enter in once into the holy places, age-during redemption having obtained; [13] for if the blood of bulls, and goats, and ashes of an heifer, sprinkling those defiled, doth sanctify to the purifying of the flesh, [14] how much more shall the blood of the Christ (who through the age-during Spirit did offer himself unblemished to God) purify your conscience from dead works to serve the living God? [15] And because of this, of a new covenant he is mediator, that, death having come, for redemption of the transgressions under the first covenant, those called may receive the promise of the age-during inheritance, [16] for where a covenant [is], the death of the covenant-victim to come in is necessary, [17] for a covenant over dead victims [is] stedfast, since it is no force at all when the covenant-victim liveth, [18] whence not even the first apart from blood hath been initiated, [19] for every command having been spoken, according to law, by Moses, to all the people, having taken the blood of the calves and goats, with water, and scarlet wool, and hyssop, he both the book itself and all the people did sprinkle, [20] saying, 'This [is] the blood of the covenant that God enjoined unto you,'
So what is the "holy place"? It is, like everything else, Christ. Now, just as Jacob was the name of a man, and yet it was also the name of all of Abraham's chosen seed, so Christ is a single person, but much more importantly, Christ is also a corporate entity. That corporate entity is "the holy place."
There are many metaphors for Jesus and all God's People, fused together by the New Covenant. For example, the God's sheep, in the care of Christ, God's vine and the branches, the City on a Hill, God's chosen King and his loyal subjects, and on and on and on. But my favorite is the New Jerusalem, the God's Lambkin and his Bride-City:
[Rev 3:12 NASB20] [12] 'The one who overcomes, I will make him a pillar in the temple of My God, and he will not go out from it anymore; and I will write on him the name of My God, and the name of the city of My God, the new Jerusalem, which comes down out of heaven from My God, and My new name.
[Rev 21:2 NASB20] 2 And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband.
The thing I find so crystal clear in John's depiction is that the Holy City descends to earth. It is described as "God's Tabernacle." IE: God's sacred space on earth:
[Rev 21:3 KJV] 3 And I heard a great voice out of heaven saying, Behold, the tabernacle of God [is] with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, [and be] their God.
For those still dismissive about this observation, notice what is outside:
[Rev 22:15 NASB20] [15] Outside are the dogs, the sorcerers, the sexually immoral persons, the murderers, the idolaters, and everyone who loves and practices lying.
That doesn't sound like heaven.
And there are twelve gates, and the dogs must be washed before they can enter the holy city. And the saints inside whisper, inviting sinners to be washed, and enter the Holy City:
[Rev 22:16-17 KJV] [16] I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, [and] the bright and morning star. [17] And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely.
Again, this is all metaphor for Christ and God's People fused together in the New Covenant.