A donor was anyone who provided biological matter, such as blood or an organ, to someone in need of it.
Karl Leonard Kelley and "Xavier Vincente Villalobos"'s passports listed them as organ donors. (PIC: "Two of One")
Cloning also involved someone being the donor of DNA to create a clone. A clone had DNA identical to the donor's, but certain cloning techniques caused a genetic degeneration, which could be detected. (DS9: "A Man Alone")
In 2268, Spock volunteered to be the blood donor for a blood transfusion to facilitate his father's heart surgery. (TOS: "Journey to Babel")
In 2366, Worf was the only suitable ribosome donor to save Patahk; Worf refused to donate and the Romulan ultimately died. (TNG: "The Enemy")
In 2371, The Doctor searched for compatible donors to give a Kazon a complete pyrocyte replacement. During the search for donors, it was discovered that Seska was not Bajoran, but Cardassian. (VOY: "State of Flux")
In 2373, Riley Frazier described the Borg Collective as thousands of donors simultaneously transferring neuro-electric energy to an injured Borg drone when necessary. (VOY: "Unity")
According to Doctor Crusher in 2379, the only way to save Shinzon would've been a complete DNA transfusion from the only compatible donor, Jean-Luc Picard. (Star Trek Nemesis)