Plain English Meaning
An oxygen system that keeps oxygen flowing the whole time it's on, instead of releasing it only when the user breathes in. The mask has a small bag attached that catches the leftover oxygen so it isn't wasted.
Full Definition
An aircraft oxygen system that delivers a steady, uninterrupted stream of oxygen from the supply source to the user's mask whenever the system is turned on, regardless of whether the user is inhaling or exhaling. Flow rate is typically regulated based on cabin altitude, and a rebreather-style mask with a reservoir bag captures excess oxygen during exhalation so it can be used on the next breath.
Context Anchor
Seen in aircraft oxygen equipment descriptions, passenger oxygen systems, and maintenance checks of masks, lines, regulators, and oxygen flow indicators.
Derivation
"Continuous" comes from Latin continuus, meaning "uninterrupted" or "holding together." The name describes exactly how the system works: the oxygen flow doesn't stop and start with breathing -- it keeps coming.