This chapter is all about how Jon Snow is an illegitimate child. (The book uses the term "bastard" but that's not Shmoop's style. Actually, both terms are kind of outdated, but because so much emphasis is put on his status of being born to unmarried parents, it's important to keep in mind.)
At a feast for the royal guests, Jon Snow plays with his albino direwolf, Ghost, and talks to his uncle Benjen, who is a member of the Night's Watch.
Jon is upset about being an illegitimate child and wants to join the Night's Watch. But Benjen thinks he's too young and the Night's Watch is a hard life for a kid.
Upset by this talk, Jon runs outside and meets Tyrion Lannister, the dwarf. Tyrion bonds with Jon and gives him some advice about turning his weakness into a strength. Or something like that – they're both a little drunk here.