Omega is the last letter of the Greek alphabet. An omega male then is the "last" man. In essence, if you were to rank all the men in the world by their virtues (bravery, intelligence, leadership, generosity, etc.), an omega male altogether would be the worst, hence "last," of all men.
Typical omega male traits include an intense interest in a particular hobby, which consequently draws his time and energies away from the conventionally 'important' things in life, like work or romantic relationships. The omega male is a fun-loving but non-aspirational individual who is reluctant to 'grow up' by embracing classic social imperatives like marriage, family and holding down a regular job.
This often-unemployed, romantically challenged loser can show up as a perpetual adolescent, or a charmless misanthrope, or a happy couch potato. He can be sweet, bitter, nostalgic, or cynical, but he cannot figure out how to be a man.