A server is just a computer. However, its hardware and software is a little different from the ones we use in our offices. A server has hardware designed to operate outside our normal PCs operations i.e its HDDs, RAM, CPU etc are somewhat made to 'endure' long hours of operations without breaking(and the hardware is expensive too). Servers also have stricter quality control, designed to do stronger work and stay long doing it. Ooh, and its hardware is optimized for any type of workload.
On the other hand, special server softwares allow for specific activities to take place, for instance, a web server will perfectly 'host' websites etc and we have many like email server, storage servers etc.
This does not mean that a normal PC can't serve as a server, when I was starting my business, I converted one of my old PCs into a web server and hosted my clients websites before I purchased an actual server. It served me for almost two years and I proudly still have it but hosts my internal accounting system.
Nowdays, there are so many things a server can do. But to sum it up, its just a PC.