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