Incarnation literally means embodied in flesh or taking on flesh. It refers to the conception and birth of a sentient creature which is the material manifestation of a force or concept whose original nature is immaterial.
As a creature type it first appeared in Judgement. Personal Incarnation from Alpha gained the subtype Incarnation retroactively.
Judgement cycle
Genesis and Glory are incarnations with similar abilities, but are not part of the cycle.
Lorwyn cycle
Inspired by the original cycle, Lorwyn had a cycle of rare Elemental Incarnations