Most people making this claim have some- or several- traits at the limits of standard human genetics; some are outside the range. Examples are pointy ears, fur, and unusually acute vision, but many more are possible and documented.
Some, but not all, Otherkin have difficulties relating to "normal" people; many have very different ethics, and some have trouble understanding human morals.
As many Otherkin can fit into society with little trouble- holding their own beliefs, but not expressing them. The most common situation, however, is that such a person can function in society, but is very different from most people, including unusual opinions, methods, theologies, ideas, etc.
Types of Otherkin
Trans-speciated Otherkin
Trans-speciated Otherkin believe that they were, somehow, born in a body of the wrong species. Reasons vary. Some, but far from all, trans-speciated Otherkin have past-life memories consistent with spending a previous life as such a being. Many, however, do not; their reasons can vary from a general feeling of "wrongness", to an intuitive knowledge, an inexplicable instinct inconsistent with being human, or something else.Genetic Otherkin
A distinct minority claim to be genetically other than human. Instead of- or as well as- the soul being inhuman, the body is. Reasons, again, vary, as does veracity.Walk-ins
A more unusual case is that of a "walk-in," when the person in question isn't actually the original owner of the body. Sometimes the original inhabitant has left for various reasons; sometimes the entities involved simply share. Due to the complexity of this topic, it is offloaded to another Wiki entry: Walk-ins.Otherkin Mentalities
NOTE: This section will never be complete.Offsite Links
There are a number of good places for information on or related to this phenomenon, or subsets of it.
These came from a kuro5hin.org submission about Otherkin:
The following have additional links: