Genesis 11:1 And the whole earth was of one language, and of one speech. 2 And it came to pass, as they journeyed from the east, that they found a plain in the land of Shinar; and they dwelt there. 3 And they said one to another, Go to, let us make brick, and burn them thoroughly. And they had brick for stone, and slime had they for morter. 4 And they said, Go to, let us build us a city and a tower, whose top may reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth. 5 And the Lord came down to see the city and the tower, which the children of men builded. 6 And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do. 7 Go to, let us go down, and there confound their language, that they may not understand one another's speech. 8 So the Lord scattered them abroad from thence upon the face of all the earth: and they left off to build the city. 9 Therefore is the name of it called Babel; because the Lord did there confound the language of all the earth: and from thence did the Lord scatter them abroad upon the face of all the earth.
He originally separated people into separate nations and parts of the world because they thought they could get to heaven apart from God. It was a punishment for their rebellion against Him and against His command to populate the earth as He commanded after the flood.
Genesis 9:1 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.
I believe the primary purpose of Israel was to be the nation through which God would show His power and sovereignty to the rest of the world and through which the Messiah, Jesus, would come.
It was also Israel's purpose to bring the gospel of Christ to the rest of the world which is why the disciples were originally given that task.
I believe it was also Israel's purpose to show the rest of the world how to be God's people so that they could learn from them, but they ultimately failed to live up to that purpose. So, Jerusalem and its temple buildings ended up being destroyed and the kingdom of God was taken away from unbelieving Jews (Matthew 21:43-45) and given to a nation that was faithful and willing to obey God and follow His Son, which is the Israel of God or the church (the body of Christ). What happened to Israel in 70 AD is a lesson for the rest of the world to learn from. Any people who rebel against God will be punished. Jesus will take vengeance on all unbelievers when He returns (2 Thess 1:7-10) because God is serious about unrepentant sin and rebellion and will punish people for it just as He punished the Jews for their rebellion long ago.
The body of Christ is the church. It consists of God's people who belong to Christ. Its purpose is to be the people of God and to serve Christ throughout the world now and for eternity.