At the end of high school I wanted a cool internet name to use when I left that hellhole and went to college. Then I got one of those hidden word things in french class and saw the letters A,E,S,G,I,X all lined up and I went "...Huh...if I remove the s....Aegix...Wow, that is AWESOME!". And then I added the "Drakan" on afterwards since I love dragons.
So it doesn't really mean anything in particular.
But I like to think it means "Age of Dragons". Which also works since the shorter version of "Aegix" is "Age"