How do Perl method attributes work?

A little known built-in Perl feature is attributes. However, the official documentation is doing a rather bad job introducing newbies to the concept. At the same time, frameworks like Catalyst use attributes extensively which seems to make many things easier there. Since using something without knowing the implications sucks a bit, I'd like to know the details. Syntax-wise they look like Python's decorators, but the documentation implies something simpler.

Could you explain (with real-world examples if possible) what attributes are good for and what happens behind the doors?