A copy is essentially an artificially created person, made using samples of DNA (ie: blood, hair, fingernails, etc). They are most often used as guards or subjects of experiments. As the name implies, copies are a perfect clone with the exact abilities and appearance of the original. However, it is also possible to create a copy whose abilities and appearance are not the same as the original, but doing this would probably require using mixed samples of DNA to get the desired results (like the technique used to create chimeras).
In the anime, it was also possible to create a copy with all the memories and experience of the original, but it was not possible in the novels.
The two most well known examples of copies are Copy Rezo, created from the DNA of Rezo the Red Priest, and the numerous Vrumugun copies. It is unclear whose DNA the Vrumuguns were created from. In the novels, it is implied that Eris is the original Vrumugun, as her last name is Vrumugun and she is the one controlling them. In the anime, however, they do not say what Eris' last name is. Also, at the end of Slayers Next, we see a person who looks a lot like Vrumugun and is presumably supposed to be the original.
Other terms for copies include homunculus (plural: homunculi), clone, and small ("small" is a term for the products of older methods of making copies).