Prime lens are a very traditional form of lens,they are lighter,cheaper(in some cases) and uses less glass.They have a fixed aperture and f-stops,if u get hold of a prime lens u will find it's printed on the lens "5omm f1\8" or as according to the lens speifications.
Zoom Lens on the other hand are the modern or as some say, "powerful". In these Lenses, the f-sop varies from a very wide range,and they are more heavier and bigger and more importantly costlier because it uses more glass,Today the kit lenses that come with DSLR cameras are generally Zoom lens if u own one, u will find it's printed on the lens "18-50mm" which means that the aperture range of that lens is varying from an 18mm to 50mm wide or how wide the lens opens up to let in light and that particular lens, is not very useful in certain areas (my opinion)
Prime lens VS Zoom Lens
The most fearsome argumentys u'll find in camera stores or among photographers,haha.Basically it's a matter of opinion,In a prime lens you cannot zoom becasue it has the fixed aperture but if u can live with that,it's a really good lens but then,for every different scenario u might need to change your lens,which is i don't know bout u guys,but for me is a hassle,but again some of them are really good for low light situations and they might not be heavy,and they do make ur pockets lighter at times as well.
In a zoom lens the main bragging right is,it covers a wide range for which u dont have to change the lens,and the fact that u can zoom in, for those who tend to be lazy :P but then quality does differ in some of them if u compare ,but then it all depends on a very sujective line,cos both of them have it neck to neck.!