So a social contract is where a "persons' moral and/or political obligations are dependent upon a contract or agreement among them to form the society in which they live".
Rousseau was most famous for coming up with the term but examples have always existed and exist right now.
An example of how a social contract works would be the legal system. For augments sake, if I say you stole all my money and you deny it, instead of fighting it out with fists or me raiding your house to find it with a gun, we both put our faith in the legal system which we both agree will be more impartial, and get to the truth. I surrender my right to take matters into my own hands on the condition that you will also do the same. Why did we do this? Because there are more benefits than not having this system in place. I may not be able to get personal revenge on you for stealing my money but I also am protected from people doing the same to me. People who are born in a state metaphorically "sign" the contract when they are born in order to live in the state.
A primitive example if you want would be that two people meet in the woods looking for berries. Both have guns and are distrustful of the other. They are constantly looking over their shoulders at each other out of fear which prevents them from going about their berry gathering. Eventually they both agree to a "contract" that they will both give up their guns at the same time. They do this because whilst you do not want to give up your gun, it means that you don't have to worry about getting shot in the back so times are more productive.
The theory is the same even if people disagree on why social contracts exist. Folk like Rousseau thought that social contracts arose because at the end of the day, humans are more interested in personal liberty and life and wish to avoid conflict as much as possible. More pessimistic people like Hobbes thought it was because humans are so naturally warlike that we needed social contracts to prevent our own violent natures.
