Wai is an action of Thais to show respect to others, like in Japan they bow. Khru means teacher. Ram means dance in Thai's old tradition style. Muay means boxing.

Usually Thais prefer to call it short "Ram Muay" or "Wai Khru". Ram Muay is the way to show respect to the teachers and the trainers. Also, in past Muay-Thai usually fought in front of the king, so Ram Muay is also to show apologize to the King for the brutal on fighting.

go to http://www.sprypublishing.com/ch3_P72-87.pdf for more information.