The term incarnation was sometimes applied to the bodies/selves/lives of a Time Lord. While it was sometimes used interchangeably with "regeneration", (TV: The Keeper of Traken, Extremis) incarnations were actually the result of this process, with Time Lords regenerating from one incarnation to another.
Barring special circumstances, a Time Lord could only have thirteen incarnations, (TV: The Deadly Assassin) before their symbiotic nuclei started to break down. (AUDIO: Trial of the Valeyard) Some, like the Master (TV: Utopia, AUDIO: Eyes of the Master) and the Doctor, (TV: The Time of the Doctor) have been given new regeneration cycles, bypassing this limit.
Use of the term Edit
Looking back on their previous lives, the Doctor occasionally used the word incarnation. (TV: The Twin Dilemma, AUDIO: The Light at the End, The Chimes of Midnight, Dead London, Scaredy Cat) He also used it in reference to the Master, (TV: Doctor Who) and others used it to talk about the Doctor's regenerations, as well. (TV: The Ultimate Foe)
The Eleventh Doctor thought he had never used the word incarnation in that capacity but was proven wrong by Ally, from an alternate dimension, who played a clip from Doctor Who of the Sixth Doctor discussing his "last incarnation" in The Twin Dilemma. He conceded but claimed that the word was hardly ever used. (COMIC: The Girl Who Loved Doctor Who)
With the term being sometimes interchanged with the term regeneration, a Time Lord stating they were in their tenth regeneration would be synonymous in saying they were in their eleventh incarnation. (TV: Hell Bent)
When referring to past incarnations, the Doctor would use the plural "mes", faces or lives. (COMIC: Four Doctors) Time Lords might also use the term "bodies" or "body" when referring, generally, to either their own or other Time Lords' different incarnations. (COMIC: Doorway to Hell) On one occasion, the Sixth Doctor used the word "iteration". (AUDIO: The Light at the End)