Can you explain the difference between a prime/fixed focal length lens and one where the focal length can be varied?

With a zoom lens, you can change the focal length to zoom in or out (there’s a proper name for it but it escapes me). With a prime lens, it’s fixed – no zoom.

Because prime lenses are fixed, they can offer lower apertures and often far superior quality but mean you need multiple lenses to cater for different situations (and therefore means more lens changing). With zoom lenses, you don’t need to switch it as often but you loose out with quality and a generally higher minimum aperture.

The great thing with being able to use a lower aperture is that you get better low-light photos (but in turn less depth of field). You’d use a prime lens in the same situation you’d use a zoom.. You’d just use them differently and get slightly different results. I think Pros only use prime lenses.

With a prime lens, your legs are the zoom mechanism.

Am I correct that the monster lenses you see at sporting events are probably 300–400mm primes? These would be well suited to fast action due to large apertures and high shutter speeds.

actually they are 400mm f/2.8, 500mm f/4, or 600mm f/4. if you ever see a lens the size of a car, that is the Nikon 800mm f/4 lens for 120,000$, the other three lens go for, respectively, 8,000$, 9,000$, and 9,000–10,000$. I am speaking for Nikon only, I know Canon is cheaper.

I use both Zoom and Fixed only because I fully utilize the features of my D300. I can tell the firmwear (the camer’s brain basiaclly) to auto-focus diffrently for every one of my lens. It was about two days of sold work to get, but the pay off is more then worth it.
You also have to consider that Fixed lens don’t brake down as fast, seeing as they usually have fewer groups and fewer moving parts, in turn. The glass is usually better too, due to the fact it can be a little bit heavier here and there. Also one other factor is most Fixed lens are sealed, whether they advertise that or not. With a Zoom lens it takes more to seal it from the elements and thus, more money.