The aperture of a lens is the size of the hole in the lens that the light pass through. The size of this hole is variable – controlled by the aperture setting.
As well as dictating the amount of light thats passes through the lens (thus influencing your exposure), the secondary effect of aperture is depth of field. That is, how much of the image, from front to back, appears to be in focus.
A wide aperture, say f/4, will give less depth of field than a narrow aperture like f/22.