Think of a game such as Starcraft. Make it turn based rather than real time and move it from the computer onto a table covered with model terrain and miniature soldiers. Now you have some sort of idea about what a Table-top Wargame is all about.
Wargamers collect model armies, paint them and then battle them against other players in either one off games or extended campaigns. There are many different types of wargame ranging in genre from fantasy, historic, modern day and science fiction.
I play wargames by the company Games Workshop. The main games I play are:
Warhammer 40 000 (40k). This is a game set in the year 40 000 (duh!). The Imperium of Man has spread throughout most of the galaxy and now battles for survival against the many alien races they have discovered.
Warhammer Fantasy Battles (WFB). Set in a world of Elves, Dragons and Magic. Warhammer Fantasy pits the various races of the Old World up against each other in a constant struggle for power.
Epic 40 000. As the name suggests, Epic is a spin-off game from 40k. the idea is the same but the scale is much smaller, allowing battles between larger armies and gigantic War Engines.
Blood Bowl. A spin-off from WFB, Blood Bowl is a game of Fantasy Football and the closest I used to think I'd ever get to playing Gridiron. Blood Bowl is a cross between WFB and American Football. Teams from the various races meet on the football field and do battle (and if they remember they might run the ball for a touch down while they're at it).
Battlefleet Gothic (BFG). Another 40k spin-off, this game is set in space and the great Naval battles that occur when star-ships of the various races meet.
Inquisitor. Yet another 40k spin-off (you may notice that all the other games are based on either 40k or WFB). This game is at a larger scale and focuses on small skirmishes between individuals in their struggle to carry out their own agenda under a regime that demands total obedience.
Wargaming is an entire hobby of model making, painting and playing. As well as scenery building (cuz empty battle fields are just boring). They are also a lot of fun. If you want any more info then go to the Games Workshop Web site to get it from the source. They also have a lot of discussion forums and resources available for download.