The aperature, also called an iris, is a device inside the lens that closes from the outside in, using a series of blades evenly spaced around the perimeter of the lens. Actually, the iris is the mechanism, the aperature is the hole created by the mechanism through which light passes.
These blades, as the iris is engaged and the aperature is closed, block more and more light, thereby allowing less and less light through the lens. The measurement used to quantify how closed or open this iris/aperature is at any given time is called the F-Stop. And the higher the F-Stop value the less light is allowed through the lens. For me, I made my peace with this relationship between f-stop and light by just remembering that its an inverse relationship. High F-Stop means Dark Picture. Very bright light of course can overcome very high F-Stop values.
But thats not all the aperature does to your photography process. Overall there are 3 aspects to aperature. First, it reduces the light allowed through the lens. Second, it changes your depth of field. The lower the F-Stop the less depth of field in your image. Depth of field is basically how much of your image is in focus. At very small aperature values, like F-1 or F-2.8 you will need to choose between your subjects nose, eyes, or ears to be in focus, while at 5.6 or 8 you will get their whole head. And finally, there is a lens quality aspect. For many lenses in the price range of us mere mortals the lens is less sharp when at its extreme limits of F-Stop. So if you have a 1.4 lens, it might be sharper at 2.8 than at 1.4. Mainly though, F-Stop is considered to control Depth of Field and light transmission through the lens.
One note on another value you will see on some lenses. T-stops. A t-stop is roughly equivalent to an f-stop, but only roughly. It is a rating given to the light transmission the lens assembly is capable of. For photography this is not generally a consideration, but for filming it has some significance. A director of photography (DP) on a film crew needs to swap glass around for different shots. Each lens has its own T-stop rating. All else being equal, f-stop, shutter speed, iso, and so on, the lighting might need to be adjusted for a lens with better or worse light transmission capabilities. By marking the lens with a t-rating the DP can have this precalculated and ready to go, saving time on set which is very expensive. If lighting cannot be altered then ISO might be, or shutter speed. All depends on the situation.
So, back to aperature. Another way to think of the F-Stop and its number system is to think of the numbers as controlling the iris. The iris is the mechanism of blades that block the light. The higher the number, the more those blades get deployed into the light path.
The common Full F-Stop list goes like this:
1 — 1.4 – 2 — 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22 — 32
The way I recall it is each is the double of the one before last. So 1, then 1.4, then double the 1 for 2, then double the 1.4 for 2.8 and so on. all you need to remember is 1 and 1.4, the rest can be rebuilt from there.
Hopefully that helped and did not muddle things for you, I will add some pictures to illustrate this all as soon as I can.