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Robb needs to get his army across the Green Fork river and the only place he can do that is at the Twins, a bridge controlled by Lord Walder Frey (and protected by two identical castles on either side, hence the name "the Twins").
Although Frey is sworn to Hoster Tully, he's not the most trustworthy person, says Catelyn. Still, they have to negotiate, and since she knows Walder, she'll go talk to him.
Walder Frey is old and bitter: he's angry at (seemingly) every lord who ever slighted his house (which is all of them). He also has a lot of kids.
Catelyn returns to Robb with terms that include taking on one Olyvar Frey as a squire and marrying another Frey – whichever one Robb wants to marry. (Oh, and Arya is supposed to marry another, if she's still alive.)
For that, Walder will join his army to Robb's and let them pass over his bridge. (Can you imagine if all toll bridges involved this kind of trade?)