The final boss is the last boss of the game. He's generally the most powerful and hardest enemy. He usually has different phases where he changes his patterns. He sometimes sends enemies after you and can have a devastating attack that kills you in one shot. The final encounter sometimes involves the final boss changing forms, requiring the player to defeat the last boss multiple times.
The final boss is usually the main bad guy in a game's story. He usually has some kind of negative relationship with the main character. After beating him, the game generally ends. In modern day games, the concept of a final boss has become more sophisticated and can be more about reaching the end of a journey than it is of defeating the last antagonist.
True Final Boss
Some games feature a True Final Boss, that is, unless having completed a specific objective throughout the course of the game usually in the form of an item, sidequest, or playing on the hardest difficulty, you will never actually see it. These bosses can be updated counterparts to the apparent final boss or another character entirely, usually a background character whose ulterior motive only becomes prominent when the objectives above have been completed (Such as Ballos, from Cave Story). True Final Bosses appear most prominently in the bullet hell and metroidvania genre.
Notable Final Bosses