Magic is the use of supernatural powers to affect reality. As noted by Clarke's Law, most if not all reported cases of "magic" were actually scientific, and belief in magic is generally restricted mostly to primitive cultures. Magic was thought by these cultures to be the specialty of witches, fairies and others with special powers.
The Sycorax, for example, believed that blood control was supernatural. One member of UNIT stated that it looked like a spell was being cast. The Sycorax leader described the ability of the Doctor to grow back his hand, which the leader had cut off, as "witchcraft" (DW: The Christmas Invasion). In a similar fashion, Humans similarly found it hard to distinguish between the psychic powers and technology used by the Dæmon, Azal and the supernatural. (DW: The Dæmons)
Different versions of science also seemed magical to some races. For example, the word-based science of the Carrionites was so different to the mathematical-based science of most other races, even the Doctor initially mistook it for witchcraft. (DW: The Shakespeare Code)
