The claw is the central hub of a milking cluster — milk from all four teat cups funnels into it before continuing on to the bucket, and it has to maintain an airtight seal to keep vacuum consistent while doing so. The gasket is what creates that seal at the claw's internal joints. Over time, with repeated cleaning cycles, exposure to milk fat and cleaning chemicals, and general wear, the rubber gasket compresses and loses its sealing ability.
The telltale sign is usually a claw that starts leaking milk around its seams, or a noticeable drop in vacuum consistency during milking even though the rest of the machine checks out fine. Replacing the gasket is a simple, low-cost fix — nearly always cheaper and faster than replacing the entire claw assembly, and it's worth checking first whenever a claw starts underperforming.