The user has a tremendous lung capacity and/or ability to use the oxygen very effectively enabling them to hold their breath for extended periods of time while staying active. This may also include birdlike lungs that allow the user to keep their lungs constantly filled with fresh air.
While this ability allows one to survive extended periods without breathing, that doesn't mean they don't need air, but they can survive for longer periods without it. Sooner or later they are going to have to breathe.
Free-diving is a mundane and learnable version of this power.