If you don't know what Miniature Wargaming is, here's your primer.
As the name implies, these are games about war (as well as smaller scale combat situations). The 'Miniature' part means that real miniature figures are used, on a tabletop, to play out the battles. (Think little green army men if you still don't see it...)
The miniature figures (aka: miniatures, minis, figs) are typically made of pewter (they used to use lead) or plastic, range from 1/4" to 1.5" tall and are hand painted for realism. (For many 'gamers', collecting and/or painting these figs is the bigger part of the fun.) The tabletop is usually dressed up with scenery as well, to further the realistic look of the game. (Think little green army men on a nice model train setup and your picture is getting pretty clear...)
These are organized games, so there are rules laid down for moving your figures and fighting them against the other player's figures. Rules can vary widely in concept and level of detail from game to game, but all attempt to capture the mechanics and mayhem of real fighting. Friendly, honest players can play most games without a third party official, but many times there is such a person organizing and officiating a game. This person is called a "Game Master". Typically in any rules set, dice will figure heavily in determining exactly what happens.
From those common ideas, the games chase off in all directions. A great many are dedicated to simulating historically accurate fighting from all time periods, cavemen to modern, and on all scales, man to man skirmishing to epic battles of huge armies. These games are the oldest members of the hobby and are still the core.
Other games move off in the fantasy direction, using elves, dwarves, monsters, magic and an endless variety of other figments of the imagination. Most of these games draw their core concepts from the world of modern fantasy fiction and ancient folklore. You don't have to play many of these games, though, before seeing the ideas of J.R.R. Tolkien near the bottom of it all.
Still other games look into the future for their setting, dreaming of spaceships, robots, post-apocalyptic dark-ages, alien races, and all manner of hi-tech equipment.
The games can be played one at a time, or many can be played in a series, known as a "campaign" (classic warfare term there), where the effects of a game are carried on into the next in some way. They can be set up entirely by the game master, or they can involve the players choosing their own forces ahead of time.
It's a vast and varied hobby with a niche for just about everyone. The games run from internationally marketed systems with huge registered tournaments to simple home-cooked rules for an evening game. You'll find gamers from the occasional player who doesn't own any gaming stuff to the gaming junky with the itch to roll dice and push figures 3 or 4 times a week, when he's not in the basement painting new figs from his $400/month figure buying habit...I'm sure we can find you in that range somewhere!