I use After Effects quite a bit but I am certainly no power user. While I've used expressions in a few projects, my use has been very basic. You may be asking what the heck are expressions anyway? Expressions are based on JavaScript and provide a way of programmatically creating interactions between elements in an After Effects animation. That sentence may be scary to you, but it's really not too bad. The key is to start easy and build on your knowledge. If you are already familiar with JavaScript or programming concepts in general, you'll pick it up quick. Here are a few links you might want to check out:

MotionScript
Creative Cow tutorials
After Effects Expressions blog with good basic info
AE Enhancers Forum: Expressions section
Google groups for AE Expressions

If you know of any additional links on expressions, let us know. This should get you started and show you what expressions may be able to do for your projects.