The aperture of a photographic lens is a hole that can be adjusted to different sizes. This lets the photographer control the amount of light reaching the film or image sensor. The aperture is changed along with the shutter speed to control the amount of light that enters the camera. This amount of light is called the exposure. Typically, a fast shutter speed will not let much light in (meaning the picture could come out too dark), so the photographer will use a larger aperture to correct for this. A slow shutter speed will need a smaller aperture to stop the picture coming out too bright.
The size of the aperture is described as an "f-stop." This is a number that describes the size of the hole in relation to the focal length of the lens. A low number (such as f1.4 or f2.8) means the aperture is wide open, and lets in a lot of light. A high number (such as f8 or f11) means that the aperture is small, and does not let in as much light.