Bane suffered a vicious attack earlier in his life, as depicted in the film. This then causes him permanent severe pain. From then on, he needs to always wear the mask, as it provides him with relief from the pain:
Nolan has revealed that Hardy's audio-muffling mask is actually pumping Bane's body full of anaesthetic. "Bane is ravaged by pain from a trauma suffered long ago," he explains.
The film Bane is largely similar to early Bane in the comics. In the comics, his mask is basically a Luchador mask. In his early appearances, he had a tube that went from a device on his forearm to the back of his head. This administered a drug called Venom, which was responsible for his superhuman strength, along with providing superhuman regeneration. He later stops taking Venom, as it's highly addictive, and he attributes some of his defeats to its influence. After freeing himself from Venom, he becomes a bit more of an anti-hero instead of a straight villain that he was in his initial appearances. In addition to his strength, the Bane of the comics is a genius, having spent his youth developing his mind in addition to his physique.
His initial appearance was in the Knightfall story arc where he wears down Batman and eventually breaks his back. He accomplishes this by first releasing the inmates of Arkham Asylum. Batman spends 3 months capturing the escapees, exhausting himself in the process. Then Bane ambushes him. Bane had deduced that Bruce Wayne was Batman, and attacked him in Wayne Manor. Due to his superior strength and fighting skills, along with Batman's exhaustion, Bane defeated Batman and broke his back. This is echoed in the film, but doesn't play out exactly the same way.