What is the condition of war according to Hobbes?

It’s been many many years since I read Leviathan, so I might be a bit hazy on the details.

Basically, before any social or political arrangements existed, man lived in a state of competition without rules. The rules of a society – be they laws or customs – are part of the social compact.

With no rules to govern behaviour, each individual was basically in a constant state of fear ofr attack for their resources, and would have always been looking to attack others for theirs. That is, if I recall correctly, Hobbes’ justification for the state, basically.

He doesn’t have a particularly bright outlook on human nature, shall we say.

The summary given by @the100thmonkey is correct in all of its essentials. The condition of war is, for Hobbes, another name for the state of nature. Hobbes asks us to ask what human beings—and, just as importantly, human relations—would be like in the absence of the state and the stability it brings. Keep in mind that Hobbes does not believe there is any such thing as natural rights or non-conventional morality. So these things to do not limit us in the state of nature.

What would people be like in such circumstances, then? According to Hobbes, we would be primarily self-interested and have very little regard for the interests of others (except insofar as they might connect to our own interests). For better or worse, our needs and wants are all roughly the same. Most notably, we wish to avoid death—which instills a desire for both security against external dangers and material goods to fulfill our bodily needs. We are also roughly equal in power such that no one person can dominate the rest. Our talents may be different (some are quick, some are strong, and others are clever), but we are stuck in a sort of rock-paper-scissors game for our lives.

The fact that we all have similar needs and wants is problematic in a world marked by scarcity, resulting in a distinct possibility for conflict to arise. Competition for scarce goods leads people to come into conflict, and even those who are not in conflict must fear that others may come after them. Worse yet, there are enough people who desire to dominate others—out of lust for glory or power—that some conflicts cannot even be avoided by eliminating scarcity or abandoning one’s material goods.

All of this puts us into a type of prisoner’s dilemma. If neither of us fights the other, then we can get peace. But neither of us can risk that because if you fight and I don’t, I die. Furthermore, if I fight when you don’t, I get glory. Regardless of what you do, then, I am better off if I fight (because my choices are between war or death and glory or peace, where war is supposed to be preferable to death and glory is supposed to be preferable to peace). This makes it rational for me to fight. But the same logic applies to you as well. Therefore, we both end up fighting—which leads to war. The only thing Hobbes believes can prevent this is an external power that is greater than the individual belligerents and can enforce the peace. This, of course, is the state. And because the problem is so severe, Hobbes says that the state must be run by an absolute sovereign whom it would be insane to challenge.