Mosh is what you do in a mosh pit.
Picture this: anywhere from a dozen to a hundred angsty teenage kids listening to their favorite get-your-blood-pumping/damn-the-Man music, releasing sexual and societal frustration as well as injuring thy neighbor and getting some much-needed exercise all in one fell swoop by accelerating their bodies to relatively high velocities and crashing haphazardly into one other. Those who are adept at moshing will come back from the pit with nary a scrape, save for those received on purpose, whereas those new at the ritual will sometimes end up beaten to a bloody pulp (not purposefully either). As the mosh pit node will inform you, most moshing is done at punk music shows, though the cultivation of proper moshing can be done in many varied environments. This type of moshing is never really planned, it just sorta happens.
Although generally seen in mosh pits at punk shows across the country and world, moshing is definitely not restricted to the pit. Small-group moshing often occurs in places that it shouldn't, such as nice restaurants, crowded theaters, small elevators, you get the idea. Thrashy music is not necessary for good moshing either (though it does help); moshing can be accompanied by the yells of those involved, elevator music, or perhaps even a string quartet without any serious drawbacks. Malls, sidewalks and high school hallways are popular places for medium- to large-group moshing, where more space allows for more people and increased audience visibility. However, this sort of moshing differs from the "standard" punk show moshing in at least two ways:
Instead of being an expression of rage or frustration at the System or one's conditions, the new school of moshing can be used in juxtaposition to an apparently serious situation to accentuate said situation's inherent silliness, or can be in many ways an example of social commentary. Somewhat similar to a flash mob.
Whereas punk show moshing is always unplanned (though possibly expected), the new school of moshing sometimes benefits greatly from a well thought out mosh (things to consider: escape routes, if need be; props or music, for effect; costumes, also for effect).
Nothing is necessary except at least a couple willing people: you don't need much space, you don't need any music, and you don't even need that many warm bodies. In dire circumstances, I've been known to pull off a well-executed bit of moshing with only two other people. Even a purpose isn't required, as new school moshing can be spontaneous and unprovoked as an expression of the Here and Now.