Being the amateur photographer I am, this is not a great tutorial post on how to use aperture. I want to share what I've learned, though! Check out this chart from CVHS Photo:
During an earring shoot the other day I decided to play with my aperture a bit and set it on a super low setting. I like to use my 50mm lens when I do product shoots. (That sounds overly professional - more like 'when I take pictures of things I've made'). Anyway, these photos are the result. The self-portraits were both accidental - I was holding the camera at arm's length trying to get a good angle of my earrings, and instead captured two unplanned photos that I actually like.
I love how the camera only focuses on a few things at a time when it's set at such a low aperture. In the flower photos, only certain blossoms are in focus while the background and most of the leaves are blurred. In the self-shot, my eye is perfectly clear while the rest of my face is clouded.
Anyway, I encourage you to play with aperture, if you have a DSLR! It's fun, and you can get some really great results with it, accidentally or not.