Aperture is referring to how wide the opening in the lens is that allows light to go through. Aperture levels are given by the F-stop. F2.8 allows more light in than F4.
A larger aperture (low F numbers) gives you shallower depth of field (DOF). I smaller aperture gives you a much deeper DOF, but you have to keep the shutter open longer making the image prone to bluriness. I usually use a tripod when I have a small aperture.