Final Explosion was used against Majin Buu as a last resort by Vegeta. He bid farewell to his family, as well as Goku, then made himself explode, which causes a enormous, devastating golden-yellow explosion wave. This attack was able to destroy most of Buu's body, leaving only confetti bits behind. However, due to Majin Buu's regeneration ability, it was able to reform it's body, making Vegeta's explosion and sacrifice pointless.
There is also a belief that Vegeta may have been unable to complete the attack due to his stone form at the end of it. Buu had eaten Dabura, who had the ability to turn flesh to stone with his saliva, and because Evil Buu absorbed Fat Buu through consumption, it's possible he gained Dabura's spitting ability in the same manner. This "alternate" outcome is merely speculation although seems to explain the stone body left behind rather than nothing, especially since Vegeta's face looked surprised in his stone form. In Final Bout, he doesn't lose his health; instead it uses his whole energy bar. It is one of his strongest moves in both the anime and video games, but its usage costs him his life, with the exceptions in Dragon Ball Z: Super Sonic Warriors 2 and Dragon Ball GT: Final Bout. In Budokai Tenkaichi 2 and 3, when using the Final Explosion, Vegeta says "Goodbye Bulma, Trunks, and yes even you, Kakarot". This attack is also completely unblockable, and can inflict severe damage on the stage, and is stronger than some Blast 2 and Ultimate Blasts.Vegeta also used a scaled down version of the attack in the Vegeta Saga against Goku when he used the Kaio-ken attack. In this adaptation Vegeta didn't lose is life, as the attack was much weaker than the one used against Majin Buu.