Ancient Domains of Mystery (ADOM for short) is a roguelike game which means that it is a single-user game featuring the exploration of a dungeon complex (and in the case of ADOM a few other games of this genre: the exploration of a large wilderness area with villages and many special locations). You control a fictional character described by race, class, attributes, skills, and equipment. This fictional character is trying to achieve a specific goal (see below) and succeed in a difficult quest. To fulfill the quest, you have to explore previously undiscovered tunnels and dungeons, fight hideous monsters, uncover long forgotten secrets, and find treasures of all kind.

So far this might sound like many other computer roleplaying games like Diablo, The Bard's Tale or Ultima.
There are two major differences to roguelike games though: most roguelike games do not use any graphics but rather rely on the ASCII character set to display their surroundings.
While this might sound horrible to you, you will be surprised how quickly you start to enjoy this "primitive" type of display. Your imagination quickly will take over and you'll no longer miss those ugly hand-drawn graphical tiles that do not resemble your picture of a dragon at all. But in your imagination, that blue D will soon become the most horrible and frightening ice wyrm you can imagine. Try it out. You won't be disappointed.
A side effect of this "graphical style" is that you won't need to download much. Roguelike games are pretty small because most of their code is concerned with a very intense sort of gameplay and not some ugly graphics quickly becoming out of date. In that respect many roguelike games are far superior to commercial roleplaying games (did I forget to mention that? Most roguelike games are available for free!)
Roguelike games are very random. While almost all of them have a background for the gameplay, the dungeons, villages and other locations in the game are randomly created anew for each game. This offers a never-ending challenge as each dungeon will be different and there (almost) is no tedious "Let's try this dungeon for the twentieth time... how boring since I know all the tunnels".
Roguelike games usually do not allow you to save your character past his/her death. While this might seem overly harsh at first, you will quickly discover that this provides a level of tension unheard of in commercial games. Every decision is importand and it's a lot more exciting to explore unknown terrain, if you know that death is final.
If you've never tried a roguelike game, you should do now. You most probably will never regret it!