The term 'Alpha Male' can be defined in both a classical and modern sense. The classical definition derives from the animal kingdom and represents a physical form of dominance over other males. The alpha male lion, for example, claims sexual rights to all females, fights off other male lions to enforce it, eats first after every hunt and dominates a vast territory of land for hunting rights.
In a modern/human sense, younger males (teens, early 20s) will subscribe to the classical form. Like a lion, they will often be the strongest, most intimidating, hit on all of the women beta males
want, are usually the first to have new sexual experiences and often dominate a set territory in thier 'hunt' for new women, such as local nightclub scenes.
Older alpha males, however, will evolve the classical traits of stength, intimidation and dominance beyond the physical by gaining power over men through thier very means of living and professional reputation. A powerful business executive, for example, will hire, promote, demote and fire others according to how well they serve his own interests. Rock stars, famous actors and other individuals of 'power' hold very simular capabilities over others in thier respective professions.
Younger alpha males who cannot mature into the modern form will usually cling to the classical form of alpha-maleness for as long as possible.
Mike Tyson was the alpha-male of boxing until Evander Holyfield defeated him, while Bill Gates is currently the alpha male of the software industry.