rebreather bag
A bag connected to a character's mouth and/or nose as a form of breath play.
It is usually depicted as a rubber bag, often black, about the size of a football (either kind). The bag has a single hose, usually about 25 mm / 1" diameter, usually connected to a mask over the character's mouth. The bag captures the character's breath when they exhale, and forces them to breathe it in again when they inhale. In an animation, the bag will inflate and deflate as the character breathes. They are often shown on characters in bondage, especially full rubber bondage.
Note 1:
A rebreather bag is not the same thing as a rebreather.
Normally, characters that are underwater, or shown somewhere where they could easily dive underwater (on a boat, on the shore, etc), are using a rebreather. Real-life rebreathers look like a complicated backpack, with two relatively large hoses (40 mm / 1.5" or more diameter) that go from the backpack to a mouthpiece.
Rebreather examples: post #2857846 post #2837041
Note 2:
A rebreather bag is not the same thing as an inflatable gag.
An inflatable gag is a rubber gag, in various shapes, that is partly hollow. Air can be pumped into the hollow part to expand the gag and make it fit more tightly in a character's mouth.
An inflatable gag has a smaller rubber bulb, often black, small enough to easily fit in a human hand. There will also be a small metal valve on one end of the bulb, usually shiny, although this is not always shown. There will be a smaller hose (about 10 mm or 3/8" diameter) running from the bulb to the gag itself. If the gag is in use, it is often concealed behind a muzzle that holds it in the character's mouth.
As noted above, a rebreather bag is relatively large - much larger than a human hand - and usually has a relatively large hose. The bulb and hose for an inflatable gag are both much smaller.
Inflatable gag examples: post #2176771 post #3610276