A prime does one focal length and does it well. With no moving zoom groups to correct across a range, designers can optimise for a single view — which is why primes are typically sharper, faster, lighter, and cheaper than a zoom of comparable quality.
The headline advantage is maximum aperture. Consumer zooms commonly stop at f/3.5 or f/5.6, while primes routinely reach f/1.8 or f/1.4. That is several stops of extra light, meaning lower ISO indoors and far shallower depth of field for subject separation.
The discipline is the real argument. Fixed focal length forces you to move — stepping back, crouching, walking closer — and moving changes perspective in ways zooming never can. Many photographers find a period shooting only a 35mm or 50mm prime does more for their composition than any new body would.