Some animals live in a social structure where the most powerful male in the group is decided by either fights or very aggressive battles that sometimes end in death (in the wild). The current alpha male must defend his position from younger members. When he is too old or not strong enough to win, he loses his position in the group. Sometimes, he will die or be forced to leave the group.
The result of this is that the alpha male usually has more opportunity to mate with the available females. This system developed because strong males will produce young which have a better chance for survival.
Some animal groups which may have alpha males:
Alpha male can also refer to a high-ranked human in a group. This may be in a business setting or sometimes in other competitive areas, like sports. However, this is an extension by metaphor: humans do not have the same mating system as other social mammals. One reason is that the oestrous cycle in humans is different. This has the result that females may be sexually receptive at almost any time. Also, humans generally pair off, and alpha males do not have exclusive rights over all females in a group, except in rare circumstances.