Here's a
wikipedia article.
Maybe the best way to visualize what the game is like is to imagine a game like Disgaea spread across a much larger dungeon where visibility is limited to the room you're in or maybe a 1 or 2 grid-square radius around yourself outside of rooms.
During a turn you can choose to perform an action (such as attack, using an item, etc...) or move one grid-square. You also have one controllable character and often have to handle multiple enemies on a map, so managing the number of enemies that can attack you is important. In general enemy actions are similar to yours, but may differ depending on the enemy and the game.
These maps generally have a single, one-way exit to a deeper level where the monsters are stronger and the treasure is better. Killing the monsters gives you experience that levels you up and makes you stronger, but if you stay in a map to level up, you increase the risk that you will starve to death. Likewise grabbing items and immediately taking the stairs down reduces the chance of starvation, but increases the chance that you will meet a monster that you can't defeat and can't escape.
A Japanese twist on roguelikes is that entering a dungeon automatically puts your player character level back to level one and makes it more important to find (and keep) a decent set of equipment for the next time. Getting killed in a dungeon generally involves some penalty like losing your equipment and items.
