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1.
It's a word put together from Chillin' and Relaxing. It actually means the same. If somebody should cool down you could say he or she has to relax or has to chill out. If you decide not to choose between these to, or you haven't made a decision while you already have to say the word, you say 'Chillax'.

It could also mean having a good time with your friends.
Woo man, don't get so angry, chillax a little!

or

Hangin' out with my homies today was super chillaxed.
by Jasper Vondeling August 27, 2007
 
2.
becoming relaxed by chilling with your friends
i have been chillaxed since i went to rachels house
by naomier April 05, 2006
 
3.
hanging out with your homies
i chillaxed at mimi's house.
by Jaiyla October 28, 2005
 
4.
It means your relaxing at the same time your chillin.
I'm Chillaxed at the beach!
by Pimpilishous March 26, 2009
 
5.
to chill (to cool down) and relax at your pace
I chillaxed as I played with my pussy and smoked a joint
by Kit Kat June 23, 2006