A basic answer is that God was making a connection between the High Priest of Israel and our Messiah Jesus that is the High Priest now. And through this connection an image and prophecy of Jesus the Messiah is made.
Jesus/Yeshua, was prophesied throughout the scriptures as the Messiah. These prophecies can be seen in word and action, those prophecies that appear in action we usually refer to as a "type of Christ". Our God/YHVH has been painting a clear picture of our Messiah since the beginning, in word and action, and the death of the High Priest mentioned in Josh. 20:6 is an example. Sometimes something appears in scripture that seems arbitrary, or doesn't seem to fit in the surrounding context, like the death of the High Priest in Josh 20:6. A closer look at passages like this will reveal that it is not arbitrary at all, that God had a specific purpose for including it. What does the death of the "High Priest" have to do with someone returning home from a city of refuge? A good question because the Priest did not accidentally kill anyone, and the death of the High Priest could not atone for the person that did accidentally kill someone.
It might appear the Law of the "cities of refuge" is leaving the Law requiring blood for blood unfulfilled. This is an example of an temporary and unfulfilled Law that Jesus came to fulfill. This was a Law left unfulfilled out of mercy and justice for someone that did not deserve to die. God's Laws cannot remain unfulfilled, however it this does not remain that way.
Law of blood for blood:
Genesis 9:6 KJV Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man.
Exodus 21:12 KJV He that smiteth a man, so that he die, shall be surely put to death.
Leviticus 24:17 KJV And he that killeth any man shall surely be put to death.
Law of cities of refuge:
Numbers 35:11-15 KJV Then ye shall appoint you cities to be cities of refuge for you; that the slayer may flee thither, which killeth any person at unawares. (12) And they shall be unto you cities for refuge from the avenger; that the manslayer die not, until he stand before the congregation in judgment. (13) And of these cities which ye shall give six cities shall ye have for refuge. (14) Ye shall give three cities on this side Jordan, and three cities shall ye give in the land of Canaan, which shall be cities of refuge. (15) These six cities shall be a refuge, both for the children of Israel, and for the stranger, and for the sojourner among them: that every one that killeth any person unawares may flee thither.
Exodus 21:13 KJV And if a man lie not in wait, but God deliver him into his hand; then I will appoint thee a place whither he shall flee.
Some explain that exile is a symbol of death in Scripture, remember because of murder Cain was punished by exile:
Genesis 4:12 KJV When thou tillest the ground, it shall not henceforth yield unto thee her strength; a fugitive and a vagabond shalt thou be in the earth.
Genesis 4:16 KJV And Cain went out from the presence of the LORD, and dwelt in the land of Nod, on the east of Eden.
And Adam and Eve were told :Genesis 2:17 KJV But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
They did die spiritually and were exiled as as a result: Genesis 3:23-24 KJV Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken. (24) So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.
(Side note: Adam, Eve and Cain, all were exiled "east".)
So the person that accidentally killed someone may have actually died symbolically by being exiled to a city of refuge. That may be accurate but it does not satisfy the requirement of blood for blood.
The Laws of blood for blood and cities of refuge are reconciled by our Messiah Jesus. Because Jesus is the High Priest now, and unlike the High Priest in Joshua's time he is able to die for the sins of a murderer, intentional and accidental. How many times have we said or heard that "Jesus
fulfilled the Law"? Here is an example of a Law being fulfilled by Jesus. The death of the High Priest foretells of the High Priest Jesus the Messiah that died to fulfill all Laws and redeem those exiled.
The Law of cities of refuge teaches us about our present redemption and prophesies of our future home. Before we were redeemed by Jesus we lived in exile, now we are able to draw near to God. We are also expecting to leave this present city of refuge and enter our new home.
Colossians 1:20-22 KJV And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven. (21) And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled (22) In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight:
Isaiah 65:17-19 KJV For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind. (18) But be ye glad and rejoice for ever in that which I create: for, behold, I create Jerusalem a rejoicing, and her people a joy. (19) And I will rejoice in Jerusalem, and joy in my people: and the voice of weeping shall be no more heard in her, nor the voice of crying.
Isaiah 66:22 KJV For as the new heavens and the new earth, which I will make, shall remain before me, saith the LORD, so shall your seed and your name remain.
2 Peter 3:13 KJV Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.
Revelation 21:1-2 KJV And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea. (2) And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. [more......
The death of the High Priest allowing the return of the exiled serves to show us of the redemption that God has been preparing since the beginning.