A Monster is usually any non-human being that the player character can interact with (attack, speak with, etc). It is also used in the old D&D sense of any NPC, human or not. Traditionally, most monsters are represented by the letters of the alphabet, although mimics appear as the symbol for whatever they are mimicking and '&' is often used for demons. In games using tile graphics, they are represented by pictures of the monsters or at least something the developer figured was close enough from some existing tile set. Killing a monster is the most usual way to gain experience and they are also the source of most treasure. Monsters may have an inventory and use (some subset) of the items in the game, or they may simply drop some items on death.
The term "monster" is considered offensive to some of the dungeon inhabitants, who prefer the term "underground security and quest assistance worker".