Humans live in a bilateral world of male and female genders. As such, the notion of a third gender turns everything on its head. How would reproduction work? How would society and culture differ in such a tri-gendered existence?
For the most part, life on Earth involves asexual and sexual reproduction. This gives us two genders, male and female, as well as hermaphroditic combinations of the two.
Oh to be sure, some organisms depart from the norm here. The fungus Schizophyllum commune boasts 28,000 different sexes, an adaptation that encourages non-sibling mating and non-relative mating. See, as with sexual reproduction, it's all about genetic diversity. The single-celled Tetrahymena thermophila has seven sexes, while the slime mold Physarum polycephalum exists in more than 700 mating types, not of all of which are compatible.
But such numbers are almost too much to fathom. Let's get back to humanity's two genders and the unavoidable question, "Why not three?"
As Adam Hadhazy argues at Live Science, a lot of male/female dichotomy ultimitly comes down to the economics of biological evolution. For most mobile organisms, three genders would introduce too much inefficiency, along with added energy costs -- and all that without significant added benefit in the genetic diversity department. The pay off is far greater for more stationary organisms (as is the risk of inbreeding), which is why we see those high gender counts in slime molds and fungi.
Sci-Fi Alien Threesomes
If you turn to the world of science fiction, you'll find some wonderful ideas about how tri-gendered organisms might work -- and some of the better examples simply breakdown the human biological reproduction process into more roles.
For instance, human males offer sperm while human females offer both eggs and the womb for the fertilized egg's development. In Iain M. Banks' sci-fi novel "The Player of Games," the Azadian species feature sperm-implanting males and members of the so-called apex sex who, following copulation with males, deposit their fertilized egg into a female for gestation and birth.
Or you can think of it this way: Various male insects (and some salamanders and newts) offer a spermatophore to females that contains both reproductive sperm and a "nuptial gift" of nutrients to assist the female in the high-energy process of reproduction. In Isaac Asimov's "The Gods Themselves," we meet an alien species called the Soft Ones with the following three genders: rationals, who produce a form of sperm; emotionals, who provide the energy needed for reproduction; and parentals, who bear and raise offspring. My reading of this is that emotionals essentially provide a nuptial gift of energy while the other two genders engage in what we would think of as traditional sexual reproduction.
Three Genetic Parents
But this is where it gets interesting. Would the gift-giving gender really count as a genetic parent? Would the birthing gender of the Azadians?
For a possible answer, just consider the reality of mitochondrial transfer, in which doctors inject the cytoplasm from another woman's egg into the egg of a patent with mitochondrial disease. The aim is to eliminate mitochondrial disease from the resulting offspring, but the offspring in question essentially boasts three genetic parents. You can read more about the process in this MedPage article.
So especially with an alien reproductive cycle, one can imagine three genetic influences over offspring, but we can also easily imagine birthing genders who, like surrogate mothers, do not contribute genetically to the offspring (though they certainly may contribute epigentically). Furthermore, you can argue that non-breeding worker classes still fulfill a vital reproductive function in a hive environment. It all serves to further the genetic programing.
Man, Woman and Demon
For a supernatural example of such surrogacy, I can't help but think of this tidbit from my Monster of the Week article on incubi and succubi:
This charade would, of course, produce Satanic children. I find the myth interesting as it both forecasts artificial insemination and implies that the extra-dimensional demon contributes genetically to the offspring -- a sort of third infernal gender for human beings.