The Social Contract works off of the idea that you are in the state because you have made an agreement, or a "social contract," to be in the state, and this is evident by the fact that you are in the state, have been in the state, enjoy the goods of the state, and as such agree to the rules of the state as a tradeoff, for example, in a State of Nature, no govenment, if I want that apple you're holding, I can just kill you and take it for myself; naturally, however, if this is the case, as it is in the State of Bature, and the one rule is that there are no rules but to survive and do as you wish, then ANYONE may do as the wish--unlimited. Anyone may kill anytime they wish, anyone may steal when they are hungry, and as the best generally survive and are strongest, these people are targeted, so you live in constant fear in light of this paradox; too strong and you'll attract attention and be seen as a threat and likely be attacked by a hord afraid of your increasing strength, and too weak and people will take advantage of you and rip you apart.
Just like Diplomacy.
The Social Contract essentially states that you'll give up your natural right to UNLIMITED freedom of this nature in order to join a government with rules and with safety in numbers; you lose the right to kill whenever you feel like it or threatened by someone growing strong, but you gain a police force and Army that act as protection so you don't have to attack otehrs, and as a government allows for a pooling of resources and agreements about who gets what in society, there is no need to steal apples, we have currency, go down to the store, and exchange the money for the apple instead of every one of us just rushing the Wal-Mart gorcery isle for whatever we want and biting and clawing whoever stands in our way.
As you live in and benefit from the State, you have, the theory goes, a Social Contract with that state; it may be broken, of course, you may leave...
But then you also leave behind the benefits of the state, ie, currency for food and ample food for all, and must make it on your own in nature, where anyone is fair game and no rules or government protections or supplies are there to help. The same way you have to pay money for the right to bowl at a bowling alley, you must pay a certain due, in this case forfeiting the right to do whatever you want to the extent of killing and stealing for supplies or taking jsutice into your own hands, for the right to enjoy the goods of the state, ie, roads, pooled food supplies, homes and all infastructures in that state, protection from outside threats...
That's the Social Contract--an agreement, yes, to give up the unlimited freedoms man has in order to have order and not have to face the State of Nature, where there are no rules and anything goes, and so anyone can kill or rape or steal from you if they wish, and as this is not attractive to most people, the Social Contract and its by product, a government, are seen as the more attractive option.