I was browsing Perl.com a day or two ago and noticed in the newest CPAN releases ticker Aspect. On a whim I followed the link and found myself introduced to a relatively new programming paradigm that I had never heard of before. I thought, monks being curious creatures, that the monestary might have some interest if they weren't already aware of it.
Rather than a standalone programming style (such as OO, Functional, Declarative, Procedural, etc), AOP seems to work best as a complementary paradigm. I don't pretend to understand the full implications of what it is and what it can do (yet), but at the root it deals with the encapsulation of "Cross-Cutting Concerns".
I found it best to understand this concept best by example, and the one that comes up frequently is debugging, tracing program flow, and the like. Rather than sprinkle print statements around your code, you create an "Aspect" that gets activated at key points in your program that you specify.
Rather than calling the Aspect explicitly (which would of course defeat the point), at Aspect creation time you define "Point Cuts" where the Aspect is supposed to be called. "Point Cuts" are groups of "Join Points". These Join Points could theoretically be any well-defined program event. The current Aspect module for Perl implements Point Cuts for entering and exiting subroutines.
This is all explained much better by the modules documentation. The author, Marcel Grunauer, also has an mp3 of a lightning talk he gave at YAPC::North::America 2001.