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Robert Baratheon arrives at Winterfell with his whole family and a lot of other people. It's like a medieval version of Entourage. Robert's first act as king at Winterfell is to go into the crypts to visit Eddard's dead sister Lyanna, whom Robert loved. (King Robert's wife Cersei is not thrilled by this.)
We get to meet a lot of the king's family and people for the first time in this chapter: the Lannister kids: Queen Cersei, Jaime Lannister of the Kingsguard, and dwarf Tyrion Lannister; the royal children: Prince Joffrey, Princess Myrcella, and Prince Tommen; some other members of the Kingsguard: Boros Blount and Meryn Trant; and Joffrey's bodyguard, Sandor Clegane.
We also learn in this chapter why Eddard is raising Theon Greyjoy: it's to make sure that Theon's father doesn't rebel again. So Theon isn't just a sort of adopted son, he's also a hostage.
Just as Catelyn and Eddard guessed (in Chapter 3), Robert came up north to offer Eddard the position of the Hand of the King; but he also offers to marry his son Joffrey to Sansa. (And since Joffrey will be king one day, he's offering Eddard something pretty big. This book makes us so glad that we live in a democracy.)