What does Genesis chapter 13 mean?

In chapter 12, Abram—the man later named renamed Abraham—lied about Sarai being his wife, out of fear. As a result, God afflicted Pharaoh's household with a plague for taking Sarai. Pharaoh allowed Abram to keep the dowry he'd paid, but sent them away as soon as he realized what had happened. As a result, Abram returned to the land of Canaan with much greater wealth than he'd had before. Pharaoh had given to Abram many animals and servants, adding to Abram's growing possessions.

In fact, both Abram and his nephew Lot have such large herds that their herdsman begin to fight over the limited resources in the area around Bethel where they have settled. Abram suggests they split up instead of quarreling. Abram offers Lot the first choice of where to settle. Lot chooses the fertile lands along the Jordan river, near the town of Sodom, already famous for its wickedness. Lot's choice to live physically near (and eventually in) Sodom will cost him dearly.

After they part company, the Lord once more speaks to Abram, reaffirming and expanding on His promises. Abram and his descendants will possess all the land he can see, and those descendants will become so abundant as to be like the dust of the earth: uncountable. God promises all of this in spite of the fact that Abram, in his mid-70s, is still childless and possesses none of the land of Canaan for himself.

God instructs Abram to walk the width and length of the land, apparently as a way of taking possession of it. Abram settles south of Bethel near the town of Hebron. Specifically, he sets his tents near the great trees of an Amorite man called Mamre. Abram builds an altar to the Lord in his new home and continues to worship God there.