Alright, so chapter 13 continues with the story of Abram (later to be called Abraham. And if you haven't figured it out yet, Sarai is later to be called Sarah).
So Abram leaves Egypt, as he was forced to do by Pharaoh in the prior chapter. We see that he is (still) quite wealthy, although this is the first time it is openly mentioned that he is exceedingly wealthy.
Wealth is considered one of the promises (in the OT) from God if you obey his commands, so you could probably say that this wealth demonstrates that Abram is favored by God.
Abram and Lot have to separate because their flocks are too large. Of course, being nomadic pastoralists, their flocks almost directly equate to their wealth. Lot moves to the east, probably across the river (although I don't believe anyone knows where Sodom and Gomorrah actually were), and Abram is left in the somewhat less fertile Canaan. This is, of course, the setup for what happens next: the infamous events of when two visitors come to Sodom, and this explains why Lot was present in the city at that time. Some commentators also use it as an insight into Lot's character. In spite of his righteousness, he is allured by visions of wealth into going to the plains of the Jordan, yet because he associated with wicked men (without being wicked himself), it ends up costing him his entire fortune. But we will see more of this soon enough.
The LORD speaks to Abram again (note: no appearance this time, just a message), but while God only speaks to Abram, the content of the message escalates. Before, Abram heard: You will be a great nation, I will give this land to your descendants. Now God repeats that the land is his, but also says that his descendants will number as the dust of the earth: a rather extravagant claim. Abram responds by building yet another altar, again demonstrating his piety and devotion to the LORD. This is consistent with his prior actions.