The aperture size affects the speed of your lens. So f2.8 aperture is 1 stop faster than an f4 aperture, that is, it allows twice the amount of light to come though at the same shutter speed. So, for the same exposure, you can shoot at twice the shutter speed. i.e f2.8@1/100s = f4@1/50s. Got it? It is an advantage at low light because with a slower lens, your shutter speed may be so slow as to be intolerable. A faster lens buys you shutter speed.
Aperture size also affects depth of field (DOF), but that is a much longer tutorial, and I hope you will dig around a bit on the web and learn it for yourself. For one, a long list of photography resources on the web is listed in the sticky at the top of this forum. --> http://forums.clubsnap.org/showthread.php?t=37569
In practical terms, a f/2.8 (fast) lens enables you to use faster shutter speed in low light conditions. Most noticably the benefits of a fast lens come in for indoor sports or stage photography, when you need a fast shutter speed without flash to freeze the motion without unexposing your subject.