It is an inflatable mattress which is inflated with air, and a mattress is a bed, hence an airbed. When not in use you deflate it, fold it, and put it away. When you need it, you pump it up in the living area or wherever there is space on the floor.

I’m familiar, and I’ve used them many times. I’ve just always had privacy when using them because I was in someone extra room, so I thought it must be something else.

Normally if you have a real guest room, you just put an actual bed there: no need for an inflatable mattress. If you end up using an airbed, it's because it's going into a space that wouldn't usually have a bed there, like the living room.

That's exactly what it is - an inflatable mattress, typically placed in a room not intended to be a bedroom, and therefore lacking privacy