The act of not only relaxing while lounging in front of the TV. It goes a step further. It's the act of relaxing, while having the attitude that they will be in a state of "coolness." When you just relax, yr mind thinks about all the stuff you think you should be doing. A person who is chillaxin is worry and guilt-free, the mind is at rest and is feeling mellow.
A combination of the words chilling and relaxing. It was first used in 1993 when then University of South Carolina freshman Roy Smith was laying out his weekly study regimen on a computer in the main libraries computer lab. Short periods of hanging out were denoted as “chillaxin” on his calendar while long periods of idle time (such as weekends) were denoted as “straight chillaxin.” A neighboring student and friend noticed the term and after explanation the term was entered into the lexicon growing slowly over the next few decades. It is now considered hackneyed in use.