In the Genesis account, the call of Abraham (Genesis 12) occurs shortly after the story of the tower of Babel (Genesis 11), and has some interesting links to it. The tower builders are trying to "make a name for themselves," but God promises Abram that "I will make your name great." The tower builders want to build a city and a tower so that they will not be scattered; Abram leaves the city life not far from Babylon for the life of a nomad. The nations were formed in the chaos after the tower building ceased; the nations will be blessed through Abraham. Yahweh comments that nothing will be impossible for the people of Babel, but Abram must learn that "nothing is impossible for Yahweh."
God's call of Abraham is his answer to the problem created by the tower builders. The tower is an expression of human determination to do what we want regardless of what God intends. God told Noah to fill the earth (Genesis 9:1); the justification for building the tower is to avoid doing that. The tower depends on human initiative and ability and ingenuity (figuring out how to make bricks in a land that has no stone for building--that is why the text makes a point of their discovery that they could fire mud bricks). The builders are proud of their abilities (they are making a tower whose top reaches heaven), but God does not agree with their self-assessment: He has to come down to inspect the tower, it is so small. So God removes the source of whatever strength they have, their common language and unity (11:6), and scatters them all over the earth, to be forever frustrated in their self-serving efforts to make a permanent name for themselves. Humanity's effort to achieve its goals results in curse and futility rather than blessing--the scattered nations will never achieve anything permanent. Rebellious humanity cannot accomplish the work of God, and God cannot let it accomplish what it wants.
But God has not given up on his plan to bring blessing, so he calls Abram to form a new people. This new people will not make themselves great; God will make their names great. (Furthermore, Genesis 12:3 says more literally that "the one who thinks lightly of you will be cursed"--whoever does not agree that Abraham's descendants are critical to God's plan will not obtain God's blessing.) Abraham's family, unlike the tower builders, will not depend on their own strength; one of the lessons that the patriarchs must repeatedly learn is that manipulation and human cleverness does not accomplish the purpose of God. Through them, the blessing God intended in creation will go out to the entire world ("in you all the families of the earth will be blessed").
But Abraham's family is just one family among many; how is this going to happen? There are some hints in the Old Testament. For example, we see Abraham blessing Sodom by his rescue operation and later by intercession. Deuteronomy talks about how the nations will learn from the Law if it is faithfully carried out. The Queen of Sheba, among others, is blessed by Solomon. Elijah and Elishah miraculously save Sidonians and Arameans. But for the most part, the kingdom of Israel could not be said to be a blessing to much of anyone. The prophets talk about a great day when blessings will flow out from Israel, but that did not happen in Old Testament times.
At Pentecost, when the Holy Spirit came (Acts 2), there was another miracle involving languages. This time, instead of confusing the the languages, God made them intelligible. The old humanity breathed out self-willed arrogance; the new humanity speaks from the Spirit in praise of Jesus. (Note also the close connection the act of speaking and the word "spirit", which in both Hebrew and Greek is indistinguishable from "breath".) The old humanity was unified by its common speech, and derived its power from that unity (Genesis 11:6); the church is unified by sharing in the one Spirit, and derives its power from that unity.
The miracle of the languages at Pentecost is the beginning of the undoing of the tower of Babel, the time when the blessing that God promised to all nations through Abraham will start having a very visible effect. The blessing is, of course, primarily Jesus and the proclamation about him (Acts 3:25-26); this is what will accomplish God's goal in creation. Instead of collecting humanity together in a city dominated by a tower, God collects all nations into a single coherent people in Christ (see Paul's extensive discussion in Ephesians 2). The promise to Abraham that his name will be great has been fulfilled. God's people have a great name because what they accomplish has lasting significance; Jesus, the seed of Abraham, has the greatest possible name (Phil. 2). God's kingdom endures forever, while the tower builders are only significant today as a foil for the story of Abraham.