"In a true state of nature, indeed, all men are born equal, but they cannot continue in this equality. Society makes them lose it, and they recover it only by the protection of laws."
-- Charles de Secondat, Baron de Montesquieu, The Spirit of Laws, 1748
The state of nature is a state in which humans once lived, a state in which there was no government, or any other higher level social organization. Humans lived alone, or in small family groups. A man did not need to answer to anyone.
Well, yes, this is a bit silly. But before Darwin explained how evolution could really make good sense, philosophers theorized how humans, presumably created originally in the same form they are in now and dumped onto Earth to make their way the best they could, invented society and government. Given these assumptions, the stories philosophers made up were often surprisingly complete, clever, and radical (theologically speaking). These days anthropology has taken over the job of trying to explain how human societies evolved.
So now we mostly talk about the state of nature when studying the history of philosophy. Anthropologist do not use the phrase.
Here are three of the more famous explanations of how and why the state of nature gave rise to government:
Thomas Hobbes: In a state of nature there is a scarcity of resources (for example, food). It is advantageous for the individual to fight and steal to survive (see the tragedy of the commons). A government improves the situation by enforcing the rules and keeping people from killing each other. While the government restrict everyone, it is to everyone's advantage because it allows everyone to work together without fear that the others will try to get ahead by stabbing them in the back."
"No arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death: and the life of man, solitary, poor, nasty, brutish and short.
-- Thomas Hobbes, Leviathan, 1651
John Locke: In a state of nature there are plenty of resources to go around; no one need be hungry. But humans create scarcity by inventing money, which encourages individuals to hoard resources. Once this starts up, the government is needed to keep the peace. (Once again, the government is to everyone's advantage).
"To understand political power aright, and derive from it its original, we must consider what estate all men are naturally in, and that is, a state of perfect freedom to order their actions, and dispose of their possessions and persons as they think fit, within the bounds of the law of Nature, without asking leave or depending upon the will of any other man."
-- John Locke, Second Treatise of Government, 1689
Rousseau: In a state of nature there are plenty of resources to go around, but humans create a scarcity by inventing money. The rich must invent rules of justice to protect themselves from the poor. A government is necessary to keep the rich from taking too much advantage of the poor. (The poor aren't well off, and the rich aren't as well off as they could be).
"The first man who, having enclosed a piece of ground, bethought himself of saying ‘This is mine’, and found people simple enough to believe him, was the real founder of civil society. From how many crimes, wars, and murders, from how many horrors and misfortunes might not anyone have saved mankind, by pulling up the stakes, or filling up the ditch, and crying to his fellows: ‘Beware of listening to this imposter; you are undone if you once forget that the fruits of the earth belong to us all, and the earth itself to nobody."
-- Jean-Jacques Rousseau, The Discourse on the Origins of Inequality, 1755
And one more view of the state of nature...
Anarchism: The state of nature is an ideal that lies in our future. We hope we can outgrow our government.