An air admittance valve is a one-way vent that lets air into a drain pipe while water runs out, then closes so sewer gas cannot escape. It does the job of a vent pipe for one fixture or a group of fixtures, and it is often the plastic cap under an island or remodeled sink.
Draining water pulls air behind it. Without a vent, that suction empties the trap, the water seal that blocks sewer gas, and the drain gurgles. A roof vent supplies that air from outdoors. An air admittance valve opens under the suction, lets room air in, then drops shut by gravity once the pressure evens out. That is why it suits island sinks and remodels where a pipe cannot run up through a wall. For how the whole system works, see what a plumbing vent does.
The model codes allow these valves with conditions. Under the 2021 residential code as adopted by Dallas (Section P3114), a sink valve must meet ASSE 1051, sit at least 4 inches above the drain it vents, stay accessible, and get air, so a sink cabinet works but a sealed wall does not. Every house still needs at least one vent pipe open to the outdoors. Texas cities can amend the code, so check with your city first, as the Texas plumbing code guide explains.
The valve is mechanical, and its seal can wear or stick. A sewer smell under the sink is the usual sign it is stuck open. A slow drain is usually a clog rather than the valve. One honest limit: an air admittance valve only lets air in. It cannot release air to relieve positive pressure, so it cannot replace the main vent through the roof, and a blocked roof vent still causes problems below.