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.