An adapter refers to a component, usually made of glass, allowing two pieces of a smoking contraption to fit together and work properly, such as in a bong or dab rig. This component comes in various sizes (10mm, 12mm, 14mm) and types (male and female).
Some adapters keep a dab rig or bong from overheating, while others capture extra oil or ash to not leak into the water chamber.
If you have several bongs and dab rigs, they are unlikely to all have the same fittings. An adapter will let you use the same banger on all of your dab rigs by allowing you to use it with multiple glass pieces.