Thomas Hobbes believed that human beings are essentially ruthless competitors, with only their personal interest at heart. Living in a state of anarchy, each man would crave another man's possessions and make his life a living hell. That is why an all-powerful state is necessary.
But why should it be a hell? Cannot men co-operate spontaneously? They cannot, says Hobbes, because they fundamentally distrust one another. Suppose I did not know what my neighbour was after, and suppose he were as strong as I was. He might intend to rob me or use me as his slave. I'd need a club to defend myself, though I was not planning to attack him myself. He, seeing my club, and not knowing what to expect of me either, would feel the need to forge a sword. For fear of the sword, I'd build great walls, and a cannon just in case. In no time, both of us would be occupied with protecting ourselves most of the time, says Hobbes, instead of producing something useful. We would have fallen into the Hobbesian Trap. And, where there are weapons and suspicion, war is inevitable. So freedom and distrust lead to waste and violence.
The fact that there are so many private guards in Guatemala shows that a large part of its resources go towards this unproductive business; if the state could handle it, a far lower number of policemen would be able to serve both me and my neighbour at the same time. (A complicating issue, and a reason why this probably isn't a good example of a Hobbesian Trap, is that the police are corrupt and fail to operate effectively; some parties probably even feel forced to protect themselves against the police.) Hobbes says everyone will fall into this trap where a strong state with a monopoly on violence is lacking.
A good example of a metaphorical Hobbesian Trap is an arms race, such as the one between America and the USSR, or Iran and Iraq during Saddam Hussein, or the countries of Europe prior to World War I. Note that a politician may abuse the Trap, by exploiting the distrust of his nation with regard to other nations in order to quell internal disagreement and strengthen his own position.
Consider also the Prisoner's Dilemma: the fact that one prisoner does not trust the other causes them both to make the wrong decision, resulting in a situation much worse for each than if they had worked together.
Theft causes shopkeepers, being forced to spend money on locks and security systems, to increase the prices of their wares. The thieves in turn then have to purchase at greater cost: they need the wares in any case, and the shopkeeper's security measures prevent them from stealing the wares. So both thieves and shopkeepers are worse off than if thievery didn't exist; but, if there were no security system, thievery would again pay off, etc. etc. This is not a pure example, since it is only the thief that is homini lupus—not the shopkeeper too, as it should be in a true Hobbesian Trap.