I'm not a pro, but here is what I know about prime lenses.
Basically prime lenses are available at certain popular settings, like 50mm, 85mm and 100mm. As such, the focal length is fixed, so you cannot zoom with the lens. Since the lens has dedicated focal length, usually it has a wider aperture and sharper image quality compared to zooms.
But if you ask what is the function of a prime lens, it is used to focus the image onto the sensor/ film, just like any other lens?
Prime lenses are the first type to have evolved for the SLR type cameras. Zooms came out after them and have been taking time to evolve such that they are able to compare to the image quality of the primes, some of the high end zooms are as such.
Four other benefits that have not been mentioned already -
1. Prime lenses are usually much faster than zooms (larger maximum aperture)
2. They are much smalller and lighter than zooms hence easier to carry around
3. Primes are generally much, much cheaper than zooms that provide the same image quality
4. Most primes have been manufactured for far longer than zooms and have been improved upon over successive generations. Generally, most primes from Canon or Nikkor will be pretty well made as the manufacturers would have decades of experience working on them.
Short primes like 35f2 / 50f1.8 / 85f1.8 are great for budget-constrained hobbyist (like me) to experiment with shallow depth of field and shoot in low-light conditions. As mentioned, they are also light and portable.
Excluding olympus (which makes f2 zooms for the 4/3 system), the fastest zoom lens out there is limited to f2.8. They cost a fortune and weigh a ton...
When we get to the longer telephoto primes like the 400f2.8 / 500f4 / 600f4, those are the ONLY lenses (bar the new sigma 200-500f2.8) which give u such a large aperture at the stated focal lengths.
There are exceptions, of course, but it may be beneficial to know that there are slower primes, such as the 50mm f/1.7 or f/1.8, that can be had for a relatively cheap price. A fact, which, of course, I'm sure you already know.
100mm is 2x magnification of a 50mm lens. So yes, it can "see further away".
For pre digital, the 50mm lens was a reference to what the naked eye can see and a lot of pre AF cameras came with a 50mm kit lens. But because of cropping factor for digital cameras, the 50mm lens is now a 75mm lens for 1.5x crop, 80mm for 1.6x crop and 100mm lens for a 2x crop.
Technically, the 100mm is capable of seeing a smaller object at a larger distance than a 50mm. I'm sorry about this, and I am not trying to be rude. It's just that when I used to conduct stargazing sessions, my most dreaded question was this: How far can the telescope see? This is because a telescope has difficulty "seeing" a candle light that is 1km away, but the eye is just as capable to see stars which are tremendously far away.