An aperture is an opening through which light travels. The Lens of a camera has an opening in order to collect light and can be controlled by a device called a diaphragm. The idea is to be able to control the amount of light reaching the image sensor.
Aperture is expressed as an F/Stop. For example F 3.5. The smaller the F-stop number the larger lens opening. So F3.5 is quite a large opening where as F16 would be a small opening and only let a smaller amount of light in. This is shown below.
When looking at camera equipment and specifications one of the first things to be mentioned will be the aperture range. An example would be F1.8-F16. A fast lens would be one that has a large maximum aperture, this is due to the fact that it would be able to allow more light to the image sensor therefore allowing images to be taken with a faster shutter speed.
One of the benefits of being able to control the aperture on a camera is to change the depth of field (DOF). The DOF is the distance which objects appear in focus on an image.
If you were taking landscape photos you would want a greater depth of field so that as much of the image was in focus.
However you can achieve great effects by minimising the depth of field to isolate the subject of the image.
Other obvious benfits of controlling the aperture is the ability to take a correctly exposed photo in reduced lighting conditions, this would be done by opening the aperture. The opposite also applies.