A warrior is a character primarily focused on the art of armed combat.
Warriors are skilled with both melee and missile weapons. In a modern or sci-fi setting, he will have skills with firearms, blasters, photon grenades or whatever other arsenal is available. The warrior is also at home in armor and often has some advantage when it comes to the use of armor, especially the heavier types.
Traditionally, the warrior has a simple style of play that allows a player to quickly get into the game and learn the interface and setting without having to bother with the complexities of the spell system or even much fuss with a skill system. Some games have attempted to make the warrior "more interesting" by adding magic-like powers to the class. While this may entertain some players, it also removes the classic role of the warrior as a simple hero with a play style that is both beginner-friendly and a real change of pace for an experienced player tired of exotic wizards and fancy-moving martial artists.
Special abilities are more common and entirely non-objectionable in warrior variants. Some such variants are specialist archers or duelists using lighter arms and armor. Berserkers are warriors with the ability to lose their sense of fear and wade into battle in a deadly blood rage. Paladins and rangers are classic D&D variants which typically have magic added to their warrior powers. There are many other possible variations on the basic warrior, depending on setting. A samurai and a knight are different archetypes and NetHack has shown they can coexist in one game. A cybernetically-enhanced warrior of the future may control his weapons with a thought, even when they are disconnected from the rest of his body. A game with a great deal of NPC interaction may reinvent the warrior as an officer, a leader of soldiers, whose path to victory is carved by the blades of his followers more than his own.
Other names for a Warrior may include Fights or Armsman. Warrior may also be an encapsulating term for a group of melee fighters such as Monks, Knights, Barbarians, etc.