Arm waving
This is seen in all Dragons contrary to what you may have read. It is a sign of submission. Basically what they are saying is "please calm down, I do not want trouble" or "you are the king and I am not worth the fuss." Most people believe that if you have two dragons in the same cage(not a good idea) the one that waves is the female. This is not 100% accurate. I have seen the males wave to the females. When two males are within sight of eachother one will sometimes wave to the other.
Head bobbing
For male Dragons, this simply means I am king. If two males are within sight of each other this is a must. If both males bob aggressively then a fight may result. However, in most cases, the less aggressive male will slow bob his head, while the dominant male bobs will have lots more motion.Females do a slight nod. In new studies, some herpetologists believe they also bob to judge distance.
Beard displaying
All Beardies will display this behavior but males have much larger beards. This is a sign of aggression or showing off for the females during breeding. Both male and female beards turn black when displayed (males are much darker and some times the darkness spreads down to their shoulders).