Depth of field
Adjusting the aperture gives lots of benefits. The first and most obvious is of course that with a bigger hole more light can enter meaning you can use a shorter shutter speed. The second is related to physics. Of course doing photography is related to physics all the time. If you remember the pin hole camera that was demonstrated during physics in school (I am sure it was shown, it is such a simple demonstration). If you remember with the pinhole camera everything is in focus. Knowing that we can now apply that to our aperture. If the hole is small a bigger portion of the image (speaking loosely) will be in focus. With a really high aperture pretty much everything will be in focus. Now that can be nice some times, but most of the time that is actually not what we want. What we want is to have the object we are taking a photo of in focus, and make the observer look at it. With a low aperture it is possible to achieve just this. This is called depth of field.
When taking portraits you want a to have the person in focus, but have the background blurry to make the person stand out more. There are lots of other times when depth of field is used to get a nice photo by blurring the background.
I have a little thing to remember which way the aperture on the camera should go. "The smaller the number the smaller part of the photo is in focus". While not strictly true as such, it helps me remember which way to take the aperture when I want to achieve a specific effect.