Both English philosophers believed there is a "social contract" -- that governments are formed by the will of the people. But their theories on why people want to live under governments were very different. Hobbes believed that people were inherently combative and at odds with each other, and so created governments to ensure their secutiry. Locke, on the other hand, argued people were born as blank slates, able to discern what is good, and chose to organize societies under governments to improve life for themselves.
Thomas Hobbes published his political theory in Leviathan in 1651, following the chaos and destruction of the English Civil War. He saw human beings as naturally suspicious of one another, in competition with each other, and evil toward one another as a result. Forming a government meant giving up personal liberty, but gaining security against what would otherwise be a situation of every person at war with every other person.
John Locke published his Two Treatises on Civil Government in 1690, following the mostly peaceful transition of government power that was the Glorious Revolution in England. Locke believed people are born as blank slates--with no preexisting knowledge or moral leanings. Experience then guides them to the knowledge and the best form of life, and they choose to form governments to make life and society better.
In teaching the difference between Hobbes and Locke, I've often put it this way. If society were playground basketball, Hobbes believed you must have a referee who sets and enforces rules, or else the players will eventually get into heated arguments and bloody fights with one another, because people get nasty in competition that way. Locke believed you could have an enjoyable game of playground basketball without a referee, but a referee makes the game better because then any disputes that come up between players have a fair way of being resolved. Of course, Hobbes and Locke never actually wrote about basketball -- a game not invented until 1891 in America by James Naismith. But it's just an illustration I've used to try to show the difference of ideas between Hobbes and Locke. :-)
