Warning: The following page/section contains spoilers. Please read at your own risk.
When Greil and his crew are heading to Gallia, Greil encounters the Black Knight, one of the enemies in the game. Greil tries to kill him, but the Black Knight counterattacks him and stabs him in the chest, thus killing him. Ike will choose to revenge his father by killing the Black Knight near the end of the game.
Soon after Greil dies, Volke will tell Ike about a day that occurred in the past. On this day, Greil picked up the Fire Emblem and went crazy, killing many people, including his own wife. He also said that he (Volke) was hired by Greil to kill him if he ever touches it again.
Spoilers end here
In the instruction manual, it has a picture with Greil as a playable character. However, Greil is not a character who is ever playable, even in the bonus modes.