An incarnation was the term applied to the bodies/selves/lives of a Time Lord. While it was sometimes used interchangeably with "regeneration", (TV: The Keeper of Traken) 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 and the Eleventh Doctor, have been given new regeneration cycles, bypassing this limit. (TV: The Keeper of Traken, The Time of the Doctor)
Looking back on his 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) When referring to past incarnations, the Doctor would use the plural "mes", faces or lives.