It might help to add a quick primer on the meaning of f/ numbers and aperture and focal length and the rest.
It's pretty simple, really.
Starting with focal length...well, it's an intrinsic property of the lens. The full, unadulterated explanation can get quite convoluted, especially when you get into telephoto and retrofocus lenses and the like...but the intuitive explanation is that, if you hold a cutout the same size as your sensor the same distance from your eyeball as the lens's focal length, the field of view is the same. That is, take a piece of paper, cut out a 24mm x 36mm rectangle in it, and hold the paper 50mm from your eye and what you see in that hole will be the same framing as a 50mm lens on a full-frame camera. Now, move the paper closer, hold it 24mm away, and you'll see the same framing as a 24mm lens. Hold it really far away, 300mm, and you'll see what a 300mm lens would see.
You know how pinhole cameras work? That just that tiny little hole is enough to project an image, even though it's not especially sharp? Well, every hole actually is a pinhole camera -- that's why shadows during an eclipse become crescent-shaped. The aperture of a lens is the diameter of the hole in the lens that the light passes through. (Roughly...again, it gets complicated in real lens designs, just as with focal lengths.)
The bigger that hole, the more light gets through -- obviously. But the image gets spread out more, too, leaving less and less of it in focus and the out-of-focus areas more smeared out. It's all a matter of very simple geometry, and any introductory textbook will have illustrations that make it obvious and intuitive.
When determining proper exposure, what matters is how much light hits the sensor / film / whatever. And, again because of the geometry, it so happens that, even between lenses of different focal lengths, the ratio between the focal length and the physical size of the aperture is what determines how much light makes through the opening. A lens twice as long needs a hole twice as big to let through the same amount of light.
That ratio is expressed as the f/ number, and it's simply the focal length divided by the size of the aperture.
A 50mm lens at f/4 has a 12mm hole in the middle. So does a 24mm f/2 lens, and a 100mm f/8 lens, and a 200mm f/16 lens.
So, the bigger the f/ number, the bigger the hole you need. But you also need a bigger lens to focus the light over the whole area of that hole...and that's where things get expensive.
A 50mm f/1.0 lens has an aperture the same size as the focal length. A 50mm f/0.7 lens has a 70mm aperture, even bigger than the length of the focal length. That requires some really funky tricks with the geometry of the lenses, a hell of a lot of very high quality glass...and, even still, the results are decidedly soft.
I recently had a chance to buy a mint-condition Canon 50mm f/1.0L for $4,000. I turned it down. It's a much softer lens than the 50mm f/1.2L, which in turn is slightly softer (or, at least, no sharper) than the 50mm f/1.4. In low light, I'll get much better results with an additional stop of ISO than with that one extra stop of aperture, meaning the only remaining reason is for the super-shallow depth of field. But the depth of field is so shallow full open at f/1.0 that it's never actually sharp. You could just as easily shoot either of the other lenses wide open and apply a gaussian blur in post-production and get something that looks almost identical. Or, you could shoot at f/1.4 and smear some vaseline on a filter. Those extra thousands of dollars buys a hell of a lot of vaseline....
Cheers,
b&
