Chances are, you've at least seen the term. It refers to someone in an altered mental state creating havoc. Anything from a bunch of kids getting too crazy at a birthday party to a mass murder can "run amok." Except it can't, because the term refers to an actual psychiatric condition, albeit one that was originally restricted to certain cultures.
If you've lead a serene life surrounded by serene people, you haven't had much cause to use the term "running amok," in your everyday life. But it's easy to recognize the phrase because we hear it in everyday life. A mischievous monkey can run amok when it escapes at a zoo. A group of soccer hooligans can run amok. A psycho killer can run amok. We assume the phrase comes from some English idiom.
Instead, it comes from formal psychiatry, although it is the psychiatry of the late 1700s and early 1800s. When Europeans sent out explorers, they found societies on Pacific islands in which some individuals would suddenly go on what we would now call "spree killings." Local people attributed these attacks to possession by aggressive spirits, and therefore not the fault of the attacker. Doctor Manuel Saint Martin reports on the discovery of such killings, and the shaping of the condition.
Amok, or running amok, is derived from the Malay word mengamok, which means to make a furious and desperate charge. Captain Cook is credited with making the first outside observations and recordings of amok in the Malay tribesmen in 1770 during his around-the-world voyage. He described the affected individuals as behaving violently without apparent cause and indiscriminately killing or maiming villagers and animals in a frenzied attack. Amok attacks involved an average of 10 victims and ended when the individual was subdued or "put down" by his fellow tribesmen, and frequently killed in the process.
The term was formalized in 1849, and considered it cultural psychiatric phenomenon - the fact that it was diagnosed in societies as separate as Papua New Guinea and Puerto Rico helped. Obviously, there are spree killings in every society. While Malay and other island societies have their spree killings shaped by their culture, it's not clear that this shaping actually differentiates the mental state of "running amok" from such killing in any other society.