In a nutshell – better results.
Prime lens are maximized for a single focal length. Zoom lens are a compromised design. From a technology standpoint zooms are all about trade-offs to make the work decently through out the range but there are points within that range that work better than others.
Primes also typically are faster, meaning they have larger aperture openings for better low level light conditions or for shallow depth of field effects.
They are more compact and they don’t pump dust into the camera body like a zoom.
The trade off is switching lens more often or “zooming with your feet”. But this is a great advantage to a photographer “working the scene”. It forces one to explore a scene for the best angles.
Primes can also be cheaper as the production is simpler and the designs hold up to years of production. Some of the best bargains in photography are very sharp, very reliable and very useful primes in the “normal” range of 35mm to 50mm.
Wide to normal prime lens can improve your photography by including more of the story in the image while over-excessive zooming can remove parts of the storytelling.
Newspaper photographers have always coveted the 35mm on rangefinder cameras as the perfect length for telling the news.
Primes also make ideal lens for video capture.
If you only have a zoom lens currently and are looking to try a prime lens I suggest looking through your best photographs and taking note of what focal length they were taken at. You might find that even though you have a wide focal length on your zoom, that you have a preferred focal length – buy a prime in this focal length.