The person who asked the question specified that she seeks an exposition of the text, not deduction from theology. So looking at the context we see that Jesus has tightly coupled the administration of the keys with Peter acting as judge:
[Mat 16:19 CSB] (19) "I will give you the keys of the kingdom of heaven, and whatever you bind on earth will have been bound in heaven, and whatever you loose on earth will have been loosed in heaven."
The Jewish Encyclopedia has a great deal to say about the practice of "binding and loosing" so I refer you to the article:
Rabbinical term for "forbidding and permitting." The expression "asar" (to bind herself by a bond) is used in the Bible (Num. xxx. 3 et seq.) for a vow which prevents one from using a thing. It implies binding an object by a powerful spell in order to prevent its use (see Targ. to Ps. lviii. 6; Shab. 81b, for "magic spell"). The corresponding Aramean "shera" and Hebrew "hittir" (for loosing the prohibitive spell) have no parallel in the Bible.
The power of binding and loosing was always claimed by the Pharisees. Under Queen Alexandra, the Pharisees, says Josephus ("B J." i, 5, § 2), "became the administrators of all public affairs so as to be empowered to banish and readmit whom they pleased, as well as to loose and to bind." This does not mean that, as the learned men, they merely decided what, according to the Law, was forbidden or allowed, but that they possessed and exercised the power of tying or untying a thing by the spell of their divine authority, just as they could, by the power vested in them, pronounce and revoke an anathema upon a person. The various schools had the power "to bind and to loose"; that is, to forbid and to permit (Ḥag. 3b); and they could bind any day by declaring it a fast-day (Meg. Ta'an. xxii.; Ta'an. 12a; Yer. Ned. i. 36c, d). This power and authority, vested in the rabbinical body of each age or in the Sanhedrin (see Authority), received its ratification and final sanction from the celestial court of justice (Sifra, Emor, ix.; Mak. 23b)...
I would also point to this article on rabbinic authority on the same site which I only partially cite below. It explains the role Jesus is commending to Peter:
...As a matter of course, the Rabbinical Authority and legislative power rested with the entire body of the court of justice or rabbinical academy, and not with the president or patriarch only. Still, the more eminent the latter in knowledge and wisdom, the better he succeeded in making his opinion or propositions prevail in the deliberation; and so the newmeasure or institution was ascribed to him, or to him and his bet din (R. H. ii. 5-9, iv. 1-4; Yeb. 77a, and elsewhere). At any rate, the Nasi, or patriarch, announced the decision, proclaimed the New Moon, and represented on all official occasions the whole rabbinical body as its highest authority. The power of investing others with Rabbinical Authority was therefore presumably his exclusive privilege. It is known that from the beginning of the third century before the common era, rabbinical authorization by the patriarch consisted in the bestowal of authority and power ("reshut") to teach, to judge, and to grant permission regarding "the forbidden first-born among animals" ("yore yore, yadin yadin, yattir bekorot," Sanh. 5a). But it is obvious that this is no longer the original form of rabbinical authorization. Far more significant and expressive of the idea of Rabbinical Authority are the words used by Jesus when ordaining Peter as chief apostle, or his disciples as his successors, and undoubtedly taken from pharisaic usage: "I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven; and whatsoever thou shalt loose on earth shall be loosed in heaven" (Matt. xvi. 19, xviii. 18). This corresponds exactly with what Josephus, or rather his source, tells of the Pharisees in the time of Queen Alexandra: "They were the real administrators of the public affairs; they removed and readmitted whom they pleased; they bound and loosed [things] at their pleasure" ("B. J." i. 5, § 2). The terms "bind" and "loose" ("asar we-hittir"), employed by the Rabbis in their legal terminology, point indeed to a sort of supernatural power claimed by the Pharisees for their prohibitory or permissory decrees, probably because they could place both men and things under the ban, or "ḥerem...
So essentially Jesus was conferring on Peter the role of "Chief Justice" of the Israel of God as he promised elsewhere and the "keys" are a metaphor for authority as judge of the Israel of God:
[Mat 19:28 NASB] (28) And Jesus said to them, "Truly I say to you, that you who have followed Me [IE: the Twelve], in the regeneration [IE: of Israel] when the Son of Man will sit on His glorious throne, you also shall sit upon twelve thrones, judging the twelve tribes of Israel.
The "regeneration" referred to is the resurrection of Israel that took place in the first century beginning with the baptism/mikveh of John and ending with the ending of the age circa 70ad (see Matthew 24). The gathering and resinewing of the bones took place in the earthly ministry of Jesus and the breath was breathed into the mighty army on Pentecost. It ended with the destruction of the temple, Jerusalem and the Jewish theocracy. Now Israel is a non-covenant nation just like all the other nations. It was necessary that Israel be resurrected in order to fulfill all the promises to the fathers.
It was during this season, before the arrival of the kingdom of God that Peter acted as Chief Justice:
[Luke 22:28-32 NASB] (28) "You are those who have stood by Me in My trials; (29) and just as My Father has granted Me a kingdom, I grant you (30) that you may eat and drink at My table in My kingdom, and you will sit on thrones judging the twelve tribes of Israel. (31) "Simon, Simon, behold, Satan has demanded permission to sift you like wheat; (32) but I have prayed for you, that your faith may not fail; and you, when once you have turned again, strengthen your brothers."
The Revelation of John also refers to this period of time when Peter and the other apostles reigned with Christ:
[Rev 20:1-6 ESV] (1) Then I saw an angel coming down from heaven, holding in his hand the key to the bottomless pit and a great chain. (2) And he seized the dragon, that ancient serpent, who is the devil and Satan, and bound him for a thousand years, (3) and threw him into the pit, and shut it and sealed it over him, so that he might not deceive the nations any longer, until the thousand years were ended. After that he must be released for a little while. (4) Then I saw thrones, and seated on them were those to whom the authority to judge was committed. Also I saw the souls of those who had been beheaded for the testimony of Jesus and for the word of God, and those who had not worshiped the beast or its image and had not received its mark on their foreheads or their hands. They came to life and reigned with Christ for a thousand years. (5) The rest of the dead did not come to life until the thousand years were ended. This is the first resurrection. (6) Blessed and holy is the one who shares in the first resurrection! Over such the second death has no power, but they will be priests of God and of Christ, and they will reign with him for a thousand years.
That the binding of Satan refers to the limits placed upon Satan such that the Messiah and his Israel of God should "spoil Satan's house" is shown in this interaction:
[Mat 12:29 ESV] (29) Or how can someone enter a strong man's house and plunder his goods, unless he first binds the strong man? Then indeed he may plunder his house.
[Luk 13:32 ESV] (32) And he said to them, "Go and tell that fox, 'Behold, I cast out demons and perform cures today and tomorrow, and the third day I finish my course.
[Luk 10:16-20 ESV] (16) "The one who hears you hears me, and the one who rejects you rejects me, and the one who rejects me rejects him who sent me." (17) The seventy-two returned with joy, saying, "Lord, even the demons are subject to us in your name!" (18) And he said to them, "I saw Satan fall like lightning from heaven. (19) Behold, I have given you authority to tread on serpents and scorpions, and over all the power of the enemy, and nothing shall hurt you. (20) Nevertheless, do not rejoice in this, that the spirits are subject to you, but rejoice that your names are written in heaven."
This period of the NT judges was just to last for a period of time (IE: "a thousand years") to be followed by the destruction of Jerusalem:
[Rev 20:7-10 YLT] (7) And when the thousand years may be finished, the Adversary shall be loosed out of his prison, (8) and he shall go forth to lead the nations astray, that are in the four corners of the earth -- Gog and Magog -- to gather them together to war, of whom the number is as the sand of the sea; (9) and they did go up over the breadth of the land, and did surround the camp of the saints, and the beloved city, and there came down fire from God out of the heaven, and devoured them; (10) and the Devil, who is leading them astray, was cast into the lake of fire and brimstone, where are the beast and the false prophet, and they shall be tormented day and night -- to the ages of the ages.
[Rev 12:12 YLT] (12) because of this be glad, ye heavens, and those in them who do tabernacle [IE: the saints]; woe to those inhabiting the land [IE: natural Israel] and the sea [IE: Rome], because the Devil did go down unto you, having great wrath, having known that he hath little time [IE: 7 years].'
The new, heavenly Jerusalem that Jesus built of living stones did, as he had spoken have as its foundation Peter and the other eleven apostles:
[Rev 21:14 YLT] (14) and the wall of the city had twelve foundations, and in them names of the twelve apostles of the Lamb.