The term "alpha male" comes from the observation of herd and/or pack animals, such as wolves. In the typical animal social group, one male animal is the leader, the alpha male, and he is generally the only male who gets to breed with the females in his harem.
In these types of animal societies, there's a simple alpha/beta dichotomy of males. Alphas pass on their genes to the next generation, and betas don't unless they are lucky enough to be around a female in heat when her alpha male guardian isn't around. Then he can rape her and run away. The majority of males are betas who never father any young.
The alpha/beta dichotomy doesn't work for human males. Modern society is mostly monogamous, but with a certain amount of polygamy such that there aren't enough women to go around for every man. See my post on the woman shortage for demographic evidence.
Human males are best divided into three groups: alpha, beta, and omega. The identification of alpha males in human society isn't as clear cut as it is in an animal herd where anyone with a pair of binoculars and patient observation can identify the single alpha male in the herd. There's no bright line that seperates an alpha male human from a beta, or a beta male human from an omega.
However, one can approximate that 15% of men are alpha males who have greater success with women than average beta males. Beta males comprise approximately 70% of the population, and they are the average men who find wives, get married, and start families. If their wives cheat on them while they are married, it's probably an alpha male whom they would be cheating with.
At the very bottom of the human male hierarcy are the 15% who are omega males, the ones who are unable to find a women for a healthy normal relationship because their desirability is too low given the existence of a woman shortage. It naturally follows that if there are 117 single men for every 100 single women, then the least desirable men won't be able to find any women.
The term "beta male" has more common usage than "omega male," so I see a lot of people using the term "beta male" for men who are really omega males. But that's not going to happen any longer at this blog.