In 1660, the British fought a civil war called The Glorious Revolution. This war pitted two groups of noblemen against each other -- the royalist party (called the Tories) and the parliamentary party (the Whigs). At stake was one basic issue--whether the power of government should be vested almost solely in the king (a "strong monarchy" that made the legislature just a rubber stamp for the king) or whether the parliament should exercise the most control over governmental affairs (a "weak monarchy" that offered some power to the king but where most of the major decisions had to have the approval of parliament, and parliament could overturn the king's decisions). Although neither side wanted to give votes and power to all the citizens (that wouldn't happen for almost two hundred years), the two sides fought about concentrating power in one individuals or sharing power among many lords and dukes.
The Whigs won. From that point on, the monarch became less and less important, the parliament more and more powerful. The argument between Hobbes and Locke centers on this same question: which is a better way to govern--placing great power and responsibility in the hands of one person or allowing many people to make decisions about government action. In a way, we are still having this argument today. [Note: This is the same argument we saw in ancient Greece: between Antigone and Creon, between the warring men and Lysistrata, between his accusers and Socrates, between the sophists and Plato]
Important terms:
Natural Law--Since they live in a new age of science, both TH and JL base their arguments on "natural law," the idea that moral principles can be seen at work not just in religious texts like the Bible, but in the laws of nature. For example, natural law says that murder is morally wrong not because some book says so, but because we can see the harm killing one's own species does in the natural world. One basic tenet of natural law is that the preservation of the species (all animals act in order to preserve their genes for the next generation). Since the death of any member of a species hurts the cause of preserving that species, murder is--by its very nature--wrong.
Natural Man* -- Both TH and JL believe that human beings are social beings--we live in societies together for our mutual benefit. They speculate that at one time this was not true. At one time, they imply, humans lived separately, like hermits--each person doing whatever he wants, whenever he wants to. This is called the state of the "natural man." The natural man has no laws, no customs, and does not cooperate with other people. Hobbes says this is a state of war, the "war of all against all." If we have no laws and don't live together, each of us would be in conflict with every other person. This kind of world scares Hobbes; he believes that in that sort of environment, the life of man is "solitary, nasty, brutish, and short."
In fact, we DO choose to live in communities together because there are many benefits: we help protect each other from outsiders and from the forces of nature; we can create surplus food for ourselves through farming together (one person cannot raise enough crops to feed himself, but 100 people farming together can raise enough to feed more than 100 people); society allows people to specialize their labor, concentrating on a set of tasks they are particularly good at rather than requiring everyone to do everything for themselves (some people farm, others invent things; some people weave and make clothing, others specialize in protecting people from invaders or criminals). In order to live together, however, we give up some freedoms--we can't do just anything we want; we have to follow laws--and we have to punish people who break laws.
Which brings us to:
Self-interest -- Both these men assume that every person will act in ways that benefit themselves, even if their actions may hurt others. The difference between them is that Hobbes thinks we need a strong monarch to keep people from hurting each other (a king's self-interest is to maintain order) while Locke believes that all the people, when they join together to make a collective decision, will think not only about themselves but about the good of the whole society. Thus, they don't need a strong king to rule over them and make them mind the law--a free people will follow the law because they see that it is in their best interest to maintain order themselves.
So the question they really ask is how best to enforce:
The Essential Social Contract -- In order to live together, we must agree not to hurt each other. At the most basic level, this means "I don't hit you, you don't hit me." We have to agree to this contract and have someone to enforce it, someone more powerful than any individual. Whoever enforces this contract--whoever keeps peace in the streets by force--is the government. If a gang in a city is more responsible for keeping order than are the police, then the gang is the real government in that place. The difference between TH and JL is that TH thinks only a strong central government, with a strong police force and a strong military can enforce this social contract. JL believes that all the people, collectively, can enforce the contract together. Example: What should happen if a person is being attacked by a criminal who wants to rob her? TH thinks we need to get a police officer to intervene. JL would say it is the responsibility of each citizen to intervene to stop the robbery.
Related to this question of the social contract is
Private Property Rights -- The right to private property is the first and most essential right in a society. "Natural man" can have no property rights--if he leaves his dwelling for some reason and leaves his property behind, anyone who happens across his home can take what they want. No one can stop a person who wants to take something from making off with it. When we live in community, we have to have laws (and law enforcers) that will identify our property as ours and help us keep it. So, in addition to "I don't hit you, you don't hit me," we also say "You don't steal from me, I don't steal from you."
This kind of right is important because other rights spring from it. If I have a right to property, then I need to also have a right to free speech, freedom to carry arms, freedom to decide who sets the tax rates, etc. Unless I can say what I like, defend myself with force, and prevent the authorities from taking my property from me through taxes, I can't really have property rights. At least, that's how the freedoms we enjoy originated (and TH and JL were important voices in that process).
*Please forgive my use of the generic "he." That was the style in the 18th Century.