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.
Vader's mask was one of the most important pieces of Vader's armor, and was vital to his survival. Without it, he would die unless in the pressurized, controlled atmosphere of one of his specially-made meditation chambers. Inside the mask were many needles that poked into his flesh to interface with him. The pressurized helmet monitored and regulated Vader's body temperature, contained radiators to diffuse heat generated by the suit's electrical systems, and contained a primary environmental sensor that continually evaluated Vader's surroundings for potential hazards. Lenses filter out light that could cause further injury to Vader's damaged corneas and retinas.They also provide infrared and ultraviolet vision, enabling Vader to see clearly in complete darkness. Sensors in the Sith Lord's helmet relay environmental data, which is then displayed as peripheral readouts. When piloting a starship, such as his personal TIE Advanced x1 prototype starfighter, Vader could slide a second layer of eye shields across the mask's eyepieces.