What is the one purpose behind why believers are what they are?
The one purpose is that believers should be to the praise of His glory. God leaves them here and gives them breath day after day so they might bring praise to His glory, offering the sacrifice of praise, the work of their lips.
Les explains that Ephesians 1 ties calling, predestination, and God's purpose together: believers were called not according to works but according to His purposes, which are wrapped up in the grace of God. They were predestined according to the purpose of Him who works all things according to the counsel of His own will. Verse 12 gives the one purpose: that we should be to the praise of His glory. The reason believers are left here and receive breath day after day is to bring praise to His glory. Hebrews speaks of offering Him the sacrifice of praise, the work of my lips, which is praise to God; that is what He is looking for and the whole purpose of everything.
That we should be to the praise of his glory, who first trusted in Christ.