The aperture is literally the hole in the lens that allows light to pass to the film or digital sensor, and the camera's lens is able to control how big that hole is. This is represented as an f-stop. For example, you might see the camera display a value like f/2, f/4, f/8, etc.
The easiest way to grasp what an f-stop is, is to think of it as a fraction. Replace "f" with a "1". So f/2 would be 1/2, f/4 would be 1/4, etc. In this way, it's easy to grasp that f/2 is a larger hole than f/4 and therefore f/2 lets in twice as much light.
Different lenses have a different maximum aperture. For example, a 50mm 1.8f lens is able to have a maximum aperture of f/1.8, which is a really big aperture. You've probably seen lenses called something like 100-400mm f/4.5-5.6. This means that the lens can be adjusted between 100mm and 400mm. At 100mm, the maximum aperture is 4.5 and at 400mm it drops to 5.6. This is because of the geometry of the longer focal length in relation to the size of the hole is smaller and thus it has a smaller relative f-stop.
Because it's a lot harder to maintain a large aperture with longer lenses, the ones that do are much more expensive and are generally larger in overall size than their cheaper counterparts.