First, God's choice. We learn a lot of theology at College. One of the doctrines we learn about is called Election. Another is the doctrine of Irresistible Calling. Theologians like to give big names to everything, but both truths are easy to understand, and both are clearly seen in the things Paul says here.
Election simply means choosing.
The doctrine of Election says that in the ultimate sense, we did not choose God, but he chose us. God chose Paul from his mother's womb. The fact that we are Elect, chosen by God, gives us a lot of comfort and peace about our salvation, because our eternal life doesn't depend on our own works, or on our own ability to choose God and to keep on choosing him. The doctrine of election backs up the truth that we are saved by grace and not because of anything we do to merit salvation. God saves you, not because of what you do in this life, but because he chose to do it long before you were even born.