Majin Vegeta is the form Vegeta became when he became a follower of Babidi and gains a significant boost in his power from his influence. While having the Majin seal on his forehead, dark black lines around the eyes and increased muscle mass puffed up to the level that veins appear all over the body and face due to the intensity of the level. Vegeta's true dark nature is reawakened (hence, the Japanese Perfect File books refer to this state as "Demon Prince Vegeta"), and in turn became extremely more powerful than he was before.
Majin Vegeta usually fights at the level of Super Saiyan 2 and his power equals that of Goku at his Super Saiyan 2 level, and later to that of himself when he fights Super Buu with Gohan absorbed and Kid Buu. After Vegeta is killed by his devastating Final Explosion as a last resort to destroy Majin Buu, this form is never seen again in either the manga or anime.
Majin Vegeta's powers were on par with Super Saiyan 2's, which means a Majin transformation doubles a Saiyan's attributes. Vegeta also seemed fully capable of harnessing every last bit of power, as if he knew his limits all along without prior training.
The form later reappears in Dragon Ball Z: Shin Budokai - Another Road, as Future Babidi again uses his magic to try and brainwash Vegeta. However, unlike the last time Vegeta transformed into Majin Vegeta, this time, it was completely against Vegeta's will.