When performing compare-and-swaps, the ticket encapsulates proof that a thread observed a specific previous value of a mutable variable. It is provided in lieu of the "old" value to compare-and-swap.
Design note: Tickets exist to hide objects from the GHC compiler, which can normally perform many optimizations that change pointer equality. A Ticket, on the other hand, is a first-class object that can be handled by the user, but will not have its pointer identity changed by compiler optimizations (but will of course, change addresses during garbage collection).