An unbeatable boss is a boss the player character, and/or their party is unable to defeat. Unbeatable bosses are most prevalent in RPGs, usually to demonstrate how powerful a character is early on in the game, so that when the player is able to beat them later in the story, they enjoy getting revenge for their earlier defeat and feel like they've accomplished something major. Unbeatable bosses generally have incredibly powerful attacks that drain the player's health quickly so that they don't unknowingly waste items, MP, or time trying to do the impossible.
Beatable Unbeatable Bosses
In rare cases, it actually is possible, if incredibly difficult or unlikely, to defeat such a boss. For example, in Chrono Trigger, as part of the storyline, the player's party is confronted by Lavos, the last boss, long before the endgame. Lavos technically can be beaten here, but because he is so much more powerful than the party, it is overwhelmingly likely that he will simply wipe out the group, at which point, the story continues forward. If the player actually does manage to defeat Lavos here, usually through carrying levels forward after beating the game via New Game , then they are rewarded with a special ending congratulating them for beating the game much earlier than usual.
Another example is in Phantasy Star II where there is a boss fight that consists of three Army Eyes. This battle cannot be won because on the third turn the Army Eyes will trap the party in "plasma rings" and it is impossible to deal enough damage to the Army Eyes to defeat them before they do so without using cheats. After the party is trapped in the plasma rings, they are transported to the Gaira Satellite where the story continues on. However, if the player uses cheats and defeat the Army Eyes, they will receive a pitiful 2 experience points and won't be sent to the Gaira Satellite so the story cannot advance any further, meaning they will have to reload their game and let the Army Eyes defeat them in order to continue on with the story. Earlier in the story, players fight Neifirst, from whom Nei was cloned. While it is intended for the fight to be impossible to win with Nei (before moving onto the fight with the other three members), it is possible for her to beat Neifirst at high levels with several healing items. However, Nei still dies in the end.