It's useful for setting up little bits of code to run later, such as callbacks. You can even do object-oriented stuff with it, though Perl provides a different mechanism to do that already. You can also think of it as a way to write a subroutine template without using eval. That's what closure is all about. This only applies to lexical variables, by the way.
Dynamic variables continue to work as they have always worked.
Closure is not something that most Perl programmers need trouble themselves about to begin with.