I've head this term been used many times, but don't know exactly what it is. Could someone enlighten me? Wikipedia didn't help!

The male all the other males don't want to mess with :) typically the head dog.

A greek? ;)

The leader of the pack so to speak the guy that everyone looks up to and respects.

The term was first used by behaviorists studying wolf packs. Each male ranks somewhere among the males and each female is ranked with the females. They use the Greek letters, alpha, bata, gamma, etc. Only the alpha male and female breed. The terms are used with other species too. So the term alpha male is commonly applied to any powerful, dominant figure.

See Establishing and Keeping Alpha Position, Letting your dog know you are the boss