What is constant-specific behavior in an enum, and when would you use it instead of a switch?

Each enum constant can supply its own method implementation by overriding an abstract method in the enum, so the behavior travels with the constant rather than living in a switch elsewhere.

The classic example is an Operation enum where PLUS, MINUS, etc. each implement apply(). It's preferable to a switch because adding a new constant forces you to implement the behavior (the compiler enforces it), whereas a switch can silently fall through to a wrong default when a new constant is added.