A monster closet is a scare tactic used in Doom 3. They can be well hidden, but experienced players may note certain walls that are commonly textured as doors. When nearing a monster closet, most likely a zombie or imp will jump out and attack the player, sometimes taking them by surprise. There are exceptions when Z-secs hide inside the monster closets, but it is rarely encountered.
Monster closets can sometimes be identified when walls or other areas fail to mesh with the surrounding architecture of what you've seen so far, and can activate upon entering the room, walking up to it, or passing right by and suddenly it pops open revealing your backside to the demon. Many of these closets often have powerups directly next to them, giving the player an incentive to move themselves towards the dangerous area unbeknownst to the unwary player. Upon grabbing the powerup, or just being near it, the closet will open. Most of them will also have powerups inside them.