For Hobbes, the social contract is a contract that people make with one another that allows them to live together in a society. If people do not make such a contract, they will be living in a state of nature in which there is a war of "all against all."
In the state of nature, everyone has the right to do anything. I have the right to kill you, you have the right to kill me. But if we allow things to stay like that, we will all plunder and kill one another and life will be, as Hobbes says, "nasty, brutish, and short." Therefore, we enter into a social contract.
This contract has two parts. First, we make a contract with one another. I agree not to kill you or steal from you and you agree not to do those things to me. But then, we also need to make a second contract with some sort of a ruler. We have to give that ruler the power to force us to abide by the terms of our contract.
By giving up our rights to the ruler, we are able to live together without killing or robbing or otherwise abusing one another. This, to Hobbes, is the way the social contract works.