Alpha males tend to be the guys who are bigger and stronger than other males. They are the more attractive males, because they are the more physically capable male and are often more confident of themselves. When not God led, they tend to have more sexual partners than other males. They often play the field and sire more children, without being a father to those children. When women cheat in their marriages, it will often be with this sort of male.
Beta males tend to not be as strong or as physically capable, but they will often share more of the homelife responsibilities. Because they will take on more of the homelife, women will be more attracted to this sort of male for childrearing responsibilities. The beta male will take the tradeoff of accepting more of an equal marriage in order to be a father and husband.
See that... we had a language/definition barrier.
More precisely, alpha males are the ones which lots of women want to have sex with. Mick Jagger (in his prime), for example, was not "bigger and stronger" than other males, but he was very definitely an alpha.
Beta males are the ones that women "settle" for, when it becomes evident that none of the alpha males who she slept with displayed any interest in actually marrying her. Betas are good providers, but unexciting.
With Alpha males, it is just easier to go through a succession of bed-warmers than to go through the trouble and struggle of maintaining a relationship with any particular woman. One of my college friends comes to mind: tall, handsome, intelligent -- all the girls wanted him. I was catching up with him a year ago. He never married.