Most photographers learn the basics of aperture in regards to depth of field and light-gathering ability, but some of what you learned is probably wrong, particularly when it comes to f-stops. If you're ready to get geeky, check out this great video that explains the truth behind it all.
Coming to you from Gerard Undone, this excellent video will teach you all about how apertures and f-stops really work. You've probably learned enough to know that lower f-numbers result in higher light-gathering abilities and shallower depth of field, but the way most of us think about how that math works is actually incorrect and breaks down at more extreme focal lengths. This is because the formula for the f-number is concerned with the size of the entrance pupil (also sometimes called the effective aperture), not the aperture. In many cases, these two quantities will be fairly close in size, but at more extreme focal lengths (particularly in big telephoto lenses), they can disagree by quite a bit, which can be attributed to the magnification caused by the different lens elements in front of the aperture. The video is an interesting look at the physics at play in lenses; I recommend giving it a watch!