This stuff gets complcated, and sometimes the camera companies don't help make it easier to understand.
Focal length of a prime lens means that the only way to change how much the lens "sees" is to walk closer or back away. A zoom, instenad, let's you change the focal length, and get more or less int eh shot, without moving your feet.
"Fixed" aperture relates only to the maximum aperture of certain zoom lenses.
Evey lens has a maximum aperture. With a prime lens, it is whatever it is, at the only focal length of the lens.
With most zooms, the maximum aperture is NOT fixed. As you zoom the lens, the maximum aperture changes. For instance, it may be f2.8 at 24mm, and f4.5 at 135mm, and at different values in between.
On an expensive zoom lens with a fixed maximum aperture, it is always, for instance, f2.8, whether at 18mm or 50mm, or on a different lens, at 70mm or 200mm.
With ALL lenses, (rare exceptions you don't need to know about) there are lots of other apertures available that are smaller than the maximum.
BACK TO THE ORIGINAL QUESTION
DISCIPLINE -- when you are taking pictures for fun, or for mental stimulation, having a prime lens (fixed or single focal length) forces you to think and look and study the light, and move yourself to the right spot for the good photograph. You learn to leave the shots the focal length does not work for -- a 50mm lens is a poor lens for a soccar shot on the other side of the field -- and you learn to spot the shots the lens is good for.
EASIER FOCUS -- most/many prime lenses are faster (have wider maximum apertures) than zooms. The wider the aperture, the less the depth of field. The less the depth of field, the easier it is to tell whether or not you are in focus.
EASIER PICTURE TIMING -- depending on the light in the location, the wider aperture of a prime makes it easier to see the subject. If you are looking for an elusive smile, for instance, it's easier to see, and then press the shutter release, with a faster (brighter) lens.
BETTER LOW LIGHT PICTURES -- a faster (wider, brighter) lens lets you use a higher shutter speed, minimizing subject blur and camera shake in low light.
SHARPER -- maybe, probably, depending on what it is being compared to. I have three 50mm lenses; a Canon 50mm f1.8, a Sigma 24-135 and the Canon 18-55 kit zoom. 8x12 prints from all three are pretty close to identical at f8 and f11, but the 50mm prime is better, obviously, at f2.8 and f2, because these settings are not on the two zooms.
BAK