In most of the games made by Squaresoft, now known as Square-Enix, and sometimes just known as Square, there were optional bosses. These games being the Final Fantasy series, as well as several other games of the same mold. The boss is also, as implied, optional, meaning that defeating it is not necessary for unraveling the twisted knot of gameplay and plot that is your typical Squaresoft game. And of course, such a thing does not only occur during Squaresoft games, but they were probably the company that originated it (as far back as War Mech in the original Final Fantasy) and perfected it.
Other than being optional, the other feature of an optional Squaresoft boss is it being very, very difficult. They are typically more difficult than the actual plot and gameplay boss, sometimes by degrees of difficulty and complication. They are also often found at the bottom of an optional dungeon, which is often exceedingly difficult, in terms of difficulty and complication.
Beating a optional Squaresoft boss will often net the player some type of exceedingly, game-breakingly powerful weapon or item, although by that point, it is not much of a reward, since there is no need for such power, because the player just beat the optional boss that is by far the most powerful thing in the game.
Like most things in a Squaresoft game, defeating the optional boss is a combination of lots of level grinding, and figuring out the exact combinations of weakpoints and stratagems that it can be defeated with. Also, often, pressing the same button over and over and over again. For an example of the type of tedium that is required to beat a Final Fantasy boss, I will use the example of Shinryuu from Final Fantasy V. Shinryuu, being a dragon, can be defeated by (amongst many other prerequisites) obtaining a special anti-dragon weapon. Which itself must be stolen from an enemy that only appears occasionally, and then which can only be stolen from successfully one time out of ten. And so on: it takes about an hour of wandering around mashing buttons before having stolen enough weapons to defeat our ancient dragon boss.
All in all, the optional bosses are the type of tedium that leaves non-fans of the entire menu-driven RPG genre even more confused about the appeal. Why, after hours of button-mashing to reach the end of a space opera plot that doesn't make sense in the first place, would a player go on to mash more buttons just because? Other than bragging rights, I think that the inclusion of an optional boss is a way to let players off easy. After the rushing delirium tremens of One Winged Angels and rifts in reality, the player might feel let down, disappointed, and some time chasing an additional goal, no matter how pointless, is a little shot of Librium to let them down to reality nicely.