Aperture is a measure of how much light gets into the camera, essentially, the size of the hole that lets the light in. It's measured in f-stops.
From a functional perspective, my easy way to think of aperture is "how wide of a plane are you focused on?" A small f-stop number (i.e., f/1.8) means a LOT of light and more of that beautiful bokeh, or blurry background. Bokeh is lovely, but if you're only focused on half the people in the picture and the rest are fuzzy, your f-stop number is too low.
I personally think AP/AV is a great place to start because aperture can dramatically change the look of a photo. In this mode, you set the ISO and aperture, and the camera controls the shutter speed.