Their names come from two French astronomers, Charles Wolf and Georges Rayet, who discovered the first known star of this kind in 1867.
Wolf-Rayets come in two flavours: WN (emission lines of helium and nitrogen) and WC (carbon, oxygen and hydrogen).
Stars like our Sun evolve into more massive red giants as they run out of hydrogen to burn in the core. When these stars begin to shed their outer layers, they behave somewhat similarly to Wolf-Rayets. So they're called "Wolf-Rayet type stars", although they're not exactly the same thing.