Theon Greyjoy is the last surviving son of Lord Balon Greyjoy and as such is next in line to rule over the Iron Islands. He is the ward of Eddark Stark upon the opening of the series.
Theon Greyjoy is the third son of Balon Greyjoy who rules over one of the smaller, poorer kingdoms of Westeros, the Iron Islands from the castle known as the Pyke. The Iron Islands consist of a group of small islands off the far west coast. The islands are not much more than stony outcroppings with little arable land. Hence most of the inhabitants, who refer to themselves as Ironmen, work the sea. This includes fishing as well as more violent pursuits such as piracy and raiding.
Reflecting this nautical background the symbol for House Greyjoy is the squid. And the words of the house are You Can Sow reflecting their less than complimentary view of those who work the land. Balon Greyjoy rebelled against the rule of Robert Baratheon nine years before in the hopes that the cost of putting down a rebellion by a poor but hard to conquer kingdom would grant the Iron Islands their freedom and consequently the freedom to raid the western coast of Westeros again. King Robert thought that any such rebellion would show him to be weak which could lead to other insurrections so instead acted to crush the rebellion. Lord Balon lost his two eldest sons in the rebellion before submitting to King Robert.
As part of the peace agreement, Lord Balon agreed to send off his remaining son, Theon who was eight at the time, to be raised as the ward of Eddard Stark with Theon's elder sister, Asha, remaining behind at the Pyke. Wards are meant to be raised as part of the family that agrees to house them and in some sense meant to bring ruling families closer together through common activity but their real purpose is to have a ready made hostage should a lord decide to rebel.
Theon seems to respect Eddard Stark and is good friends with Robb Stark but is well aware that he is in some sense just a glorified prisoner. He does like pointing out the fact that to Jon Snow while he isn't family he is still treated better than Jon is. Theon bristles against the cautious nature of the Northerners and seeks adventure. He is also somewhat worried about his standing, since while in Westeros titles usually flow through the male line it is not unheard of for the Greyjoys to give titles to women who have proven themselves and while Theon has been at Winterfell his sister has been at the Pyke.