A monster is essentially any nonhuman creature that can attack or physically oppose characters, such as by stealing an item or escaping. In game design, a monster is a kind of character that consists of mainly the traits required to use it in an encounter. In fact, humans can be "monsters" in that sense.
In classic D&D, monsters did not have the same kinds of traits as PCs. An encountered creature with the same abilities as a member of a PC class was instead termed an NPC. Dungeons & Dragons Third Edition made monsters more PC-like, while Dungeons & Dragons Fourth Edition dialed the differences back even more.
In point-based games such as GURPS or Hero System, monsters may lack detailed point totals, or may simply lack detailed trait lists unrelated to their role in the scenario. For instance, animals can not do a lot of things humans can, but it is usually sufficient to describe them as having animal intellects and noting whether they have a human-like ability to manipulate tools.
A monster is essentially a special kind of simplified NPC.