A prime lens is a lens which does not zoom. That is, as you say, it has a fixed focal length.
All lens design is a matter of balancing competing factors, including various optical properties which affect image quality in different ways, as well as size, weight, and cost. Zoom introduces a significant complication into this compromise: not only is it complex itself, but also, it means that the other compromises can't be made to fit just one focal length. That means that zoom lenses are usually more expensive or have lower image quality (or, sometimes, both at once). Almost always, maximum aperture is the first to go, with f/2.8 being the normal (but not universal) limit for a "fast" zoom, while many primes are f/2.4, f/2, f/1.8, or lower.
Additionally, some people find that they enjoy working with prime lenses. I won't elaborate too much on this here, but see Would a fixed or zoom telephoto lens be better for learning? and particularly How do I compose photos with prime lenses?
As for the origin of the term: it's clearly a retronym — a new word made up to cover something that didn't need its own term until something else came along. (Like, "acoustic guitar" or "land-line telephone".) In this case, that's zoom lenses: before they were popular, a lens with a fixed focal length was just a lens. If you look at this search for prime lens in books before 1960, you'll notice that the term "prime lens" is used in opposition to a secondary adapter lens which attaches in front. This makes perfect sense, and in fact we still call that kind of adapter lens a "secondary lens".
Most of these results are in cinema or industrial photography. If you extend the search through the 1960s, you'll see the same use as a distinction for "the main lens that you might attach an adapter to", and increasingly in still photography. One particularly interesting snippet (full book not online) describes a zoom lens design like this:
In its simplest form the zoom assembly may be thought of as a combination of an afocal attachment of variable power placed in front of the remainder of the components composing a prime lens.
And there are similar quotes in other books from around the same time.
This very well may be the bridge by which the term entered the popular vocabulary — by 1978, there are articles talking about "prime, fixed-focal-length lenses" as opposed to zoom lenses. By the early 1980s, the usage we are familiar with now is commonplace.