He's only seen without it on two occasions. The first is in TESB, very briefly, from behind, when he's in his quarters apparently undergoing some sort of medical procedure, possibly a regular necessity to maintain his metabolism. The second time is in the final scenes of ROTJ, when he's dying after his confrontation with the Emperor. He asks Luke to take it off because he wants to look at him with his own eyes. Luke is reluctant, telling him that he'll die, but Vader insists, so Luke takes it off (knowing how to, without being told, but anyway...). There's a hiss of released pressure, but otherwise we see nothing to suggest what the helmet does for Vader, or why it's essential for his survival.
In short, the mask controlled the pressurized atmosphere Vader required for his survival. It also provided the interface with the sensors (though, why the needles had to be in his face versus any other part of his body is a good question). It also effectively boosted his sensory perception (via external sensors) and corrected his vision which had been damaged.