Amateur radio, also called ham radio, is an internationally recognized radio service; technically speaking, two services. In its Radio Regulations the International Telecommunication Union (ITU) defines the amateur service as
“[a] radiocommunication service for the purpose of self-training, intercommunication and technical investigations carried out by amateurs, that is, by duly authorized persons interested in radio technique solely with a personal aim and without pecuniary interest.”
Consistent with how the ITU defines all other radio services there is a separate “amateur-satellite service” definition:
“A radiocommunication service using space stations on earth satellites for the same purposes as those of the amateur service.”
Read an overview, giving more information about amateur radio here.
Also available in Español (Spanish).