What is a boss?

(Geek) historical and cultural fact: the first game in which a boss appeared was dnd in 1974. In this dungeon-crawl RPG, a golden dragon was keeping the last treasure of a dungeon.

In single-player games, a boss is used to ensure a player has taken the time to level-up (raise their abilities through fighting anonymous easier foes) before progressing to a new section of the game. A boss is also a closure of Gameplay Progress according to Staffan Björk and Jussi Holopainen in Patterns in Game Design, p229.

A boss is usually bigger than the hero. As an example I found a kind of evolution in the difficulty of Doom II monsters:

• the Imp (brown) throws fire balls but can be killed in one shot (60 HP)
• the Hell Knight (light brown, horns) needs a bit more work (500 HP)
• the Baron of Hell is really resilient (1000 HP)
• and finally the Cyberdemon has an audible step when he moves (4000 HP)

In the early levels, the player may consider a Hell Knight as a difficult monster, maybe an end-of-level boss. But in the last levels, Hell Knights are very common. The player has become used to it and has possibly found a strategy to kill them (a particularly relevant one can be monster infighting). Only the Cyberdemon could be considered as a real big boss: it appears once or twice in the whole game (I remember having encountered it at least once with the ultra violence difficulty level). Anyway, the encounter with this boss (particularly in the 8th level) should teach the player that he/she should use monster infighting to be able to kill difficult monsters. The same principle is followed in Dildo Tank: the end-of-level boss is a common monster in the next levels, but the player knows which strategy to follow to beat them, and even sometimes many of them at a time. Bosses teach the player some play skills.

By the way, from an art design perspective, the monster sprites are set once and for all. As the player progresses in the game, there is no need to add new sprites: the previous end-of-level boss's sprite still fits "normal" monsters. This makes the art designer focus on fewer but higher quality monster appearances.

On another hand, a boss is an element of the scenario/storyline. In Wario Land III, killing a boss sometimes gives a music box, but ending a level gives a new power like swimming or brawling. In Mystic Quest, battlefields (see screenshot nearby) can help the player earn more experience before trying to enter a dungeon and kill the boss at the very bottom of the dungeon. This is rather a grinding/bashing solution which is not really pleasant as it does not really teach the player anything, but simply increases the level of the character.