Aperture...

An aperture is a hole. In terms of your camera, the relevant hole is the one that lets light from the lens into the camera and onto the sensor where images are captured. I use aperture in two ways:

1. To let more light in when I'm shooting in dark conditions, e.g., at night
2. To control how deeply object are focused in my pictures.

The first one is simple enough: choose a low aperture number (also called "f number") so more light gets to the sensor. I explain how to set aperture further down in this post.

The second one takes a bit more explanation (but only a bit). With a low aperture number, you can focus on something in the foreground, like Grandma, and the background will be out of focus so Grandma really stands out. With a high aperture number, things close to you and far away from you will be in focus in your pictures. Use this one when you're shooting landscapes. Smarty pants like to refer to how deeply things are in focus as "depth of field". Google this phrase for more info.

See below the same picture taken with a low aperture number (blurry background) and a high aperture number (more stuff in background in focus). The lights on the tree in the background are particularly illustrative.

To manipulate the aperture number, you have to use one of the "creative zones" on your Canon DSLR. On my Rebel XT, I use Av mode. Don't ask me why (yet), just use it if you want to play with aperture! By the way, in this mode you control the aperture number with the "wheel" on top of the camera (in the picture below, in the lower right behind the shutter button). The aperture number shows up in the display on the back of your camera, probably to the left of the number showing how many pictures you can take. Something like this: 3.5 [311]

3.5 would be a low aperture number. Spin the wheel (in Av mode) and you'll see this number change from 3.5 to around 22 (on my Rebel XT anyway).
BTW, I recently had a friend who was having trouble with his DSLR. It seems only the right side of the pictures he was taking was in focus; the left, not so much. I discovered that the problem was really that the aperture was set to a very low number. This meant that, for whatever reason, the camera was focusing on stuff on the right and everything closer to and further away from its focus point was fuzzy.