First, just so we know we are all on the same page, aperture is the opening in the lens that lets the light through into the camera body. In almost all cameras this opening is variable and can be adjusted. The measurement for the opening is called the f-stop. This is where we could jump off the cliff into sheer geek heaven, but I will resist. At a high level the number you are looking at is a fraction. It is the ratio of the opening to the focal length of the lens. This is why it is always written as f over something. So you might have f/8 or f/3.5. See how the number is at the bottom of the fraction? This is why the smaller the number the bigger the hole. So if you have a smaller f-stop you have a wider opening. It is one of those funky math things. OK, pressing the geek off button now.
So the first thing we can see is that the aperture is something that is in the lens. The size of the aperture is always a function of the lens, never the camera body. Just like shutter speed is all about the camera body and not the lens. Oh, I am talking specifications of equipment here. It made sense in my mind... haha. When lenses are put together then each one will have certain limitations of aperture. When you purchase a lens you will see an f-stop listed for that lens. The value listed will always be the widest that the aperture can open up. Typically people really don't worry about how far they can stop down a lens. They want wider open most of the time. So you have to dig deeper into the specs to find the smallest the aperture will go.
The fastest lenses.... oh wait, maybe I should explain fastest here. Photographers will refer to a lens as either fast or slow. This is not an indication of how quickly you can put it on and off the camera. They are actually talking about how wide the aperture will go. The wider the aperture will go then the faster you can set the shutter speed for a proper exposure, everything else being the same. So the aperture of a lens in indirectly fast or slow because of the effect on shutter speed. Thing of aperture and shutter speed as being a tug of war or a see saw relationship. If you set a proper exposure, then you change either aperture or shutter, then the other needs to change as well but in the opposite direction.
OK, back to fast lenses. So the fastest lenses will be prime or fixed focal length lenses. (GEEK ALERT) This is all about optics and lens design and the number of elements in the lens. And.... oh wait... no geeking out. OK, you just need to trust me on the design thing. The prime lenses can simply open up wider than a zoom lens. So like my favorite lens in my bag is my 50mm f/1.8 prime lens. It is an extremely fast lens. I can get natural light shots with a decent shutter speed and a very slow ISO like this one.
This shot was able to be taken without a flash indoors just hand holding the camera. This is the benefit of a fast lens. Notice also that the background is blurry. This is a secondary feature of wide open apertures. It may be good or not depending on the photo you are taking. The other thing about primes is that they only have a single f-stop listed for the widest aperture setting. Some zooms are that way too. They will only list a single f-stop. They will also have a very big price tag.
So most zooms have two numbers listed on them. A common kit lens to go along with entry level DSLR cameras is an 18 -55mm f/3.5-5.6 lens. Ahhh see the two numbers for the f-stop? I won't complicate this with more geekyness other than saying remember how we talked about the aperture measurement being a function of the ratio between the opening and the focal length of the lens? Well on less expensive lenses the actual aperture will only open so far. Now as you change the focal length of the lens you start to change that ratio. The aperture does not actually change inside, the focal length changes. So in effect you change the f-stop of the lens without touching the aperture. In really expensive lenses they have a way to get around this to actually change the aperture as you change focal length so you can maintain the same opening to focal length ratio. So that lens I just talked about has a maximum opening of f/3.5 when you are at 18mm and a maximum opening of f/5.6 when you are at 55mm.
So here is the interesting thing. Let's say you are shooting manual mode on your camera. You are at 18mm and set yourself to f/3.5 for the aperture and say are at 1/250 of a sec for shutter speed. Then you decide to zoom all the way in for a close up. You forget to check your light meter and readjust your shutter speed. So you are now at f/5.6 at 1/250th and your picture ends up one and a third stops too dark. Opps, that was not intended or expected. If you are shooting in aperture priority then the camera will automatically adjust your shutter speed down to 1/100th of a second. If you are shooting sports you now have a blurry picture. Hmmm, this is getting a little complicated. Well that is one of the challenges of a zoom lens. I am mentioning it to make sure you stay mindful of what will happen.
This is one of the benefits of a DSLR is that you can chose a prime lens that is very fast for some shooting, and a zoom when aperture is not as important. I am a huge fan of bridge or superzoom cameras. I personally thing that Fujifilm makes the best of them. Their top of the line bridge camera is the HS20EXR. Since it is a bridge camera it does not have interchangeable lenses. So you are stuck with an f-stop range of f/2.8-5.6 on it. Not a bad lens at all. But it is what it is. Oh that camera has an effective focal range of 24-720mm. WOW!!! Talk about incredible zoom! Oh I am starting to drift from aperture.
So now you know what the term fast lens means, why some lenses have two numbers for aperture, and why some people love prime lenses. I hope this helps a bit.