Aperture refers to how much light is hitting our film or digital sensor.
Inside of a lens are a series of blades that open or close and will control how much light will be passing through the lens.
Sometimes we want/need all the light coming through the lens as we can get, while other times, we don't. We may intentionally want to reduce the light passing through, something I often do when photographing waterfalls.
Aperture also has a wonderful visual effect on our photograph, as it can control what is IN focus and what is OUT of focus.
The is called: Depth-of-Field or the more technical term: Hyperfocal distance. Yeah, I know... they love to use confusing terms.
A perfect example of a limited Depth-of-Field is a typical portrait. You know the kind, our subject is nice and sharp while the background is either slightly out of focus or completely blurred.
Aperture is defined by their "f/stop" where the smallest number means that the Aperture is wide open, giving us maximum light and a limited depth-of-field. This is beneficial when shooting in low-light conditions and also when I want to freeze the action.
By increasing my f/stop, I am closing the Aperture, thus reducing the amount of light coming through. This starves my exposure of light and increases the Depth-of-Field.
After setting the ISO, I usually set the Aperture next to directly control the depth-of-field. I then set my Shutter-Speed to whatever will bring my exposure into balance.