We learn a lot about Bran and about Winterfell in this chapter, since Bran's chief hobby is climbing over everything and seeing everything (and telling us about it).
This doesn't work out so well for him in this chapter. With most of the adults out hunting, Bran decides to climb up an abandoned, partly ruined tower (never a good idea), then overhears a man and a woman talking about politics (still not a good idea), and then sees them as they start having sex (told you so).
And who are those two people? Cersei and Jaime Lannister. This is (a) problematic, since she's married to the king (!), and (b) gross, since they're twins.
The two of them see Bran and, to make sure that Bran doesn't tell anyone what he saw, Jaime throws him off the tower. So Bran might die before he even gets a chance to name his wolf.