Otherkin are essentially people who consider themselves to be not entirely (or not at all) human, for some reason. So far there seem to be a few main viewpoints on why a particular person considers themselves something Other.
Trans-species
The most common appears to be those who feel they were born in the wrong body. Much as a transgendered person feels that they were born in a body of the wrong gender, some Otherkin feel they were born in a body of the wrong species. Frequently those concerned have past-life memories, but not always. (The nature of those memories is a topic for a different article).
Genetics
A few people claim to be not entirely human genetically. Obviously this is harder to fit into consensual reality than the transspecies concept. Many of them were born with physical variations in the extremes of human norms (pointed ears, full body fur, etc). Some have claimed infertility with "normal" humans (making them a separate species rather than a subspecies); others are crossfertile. As far as I know, the only genetic claims are for some form of Fae (generally Sidhe or Tuatha de Daanan) or angelkin.
Walk-ins
The third type are those who were not born in the body they inhabit. Sometimes the original inhabitant is still there and they share; with others, the original person has left (through near-death experience, trauma or other problem), leaving the body to its new inhabitant. The incoming entity has no more restrictions as to "species" than any other incarnate (see "trans-species" above) and thus can be something other than human.