These pics above are male Beardies showing their stuff during breeding season.
Arm Waving In younger Bearded Dragons arm waving behaviors are pretty common, usally when basking. One of the cutest behaviors i've seen in any animal. During this behavior, the Dragon stands on three legs while one arm is waved in a circle at a very slow pace. In juveniles, this display is used to appease the larger Dragons. When the Dragons grow older, this behavior disappears in males, but females use it as a form of appeasement towards the males(you'll see it alot during breeding season).
Breeding Signs Male Dragons have the most profound signs during breeding season. My dragon Lolly(he was named before I knew what sex he was)started turning black under his chin, crazy head bobbing soon followed. Those are pretty good signs of a male. Although females beards also turn a little dark they won't get black like the males. If you have two males in the tank during breeding season they will fight!!! They look like two small dinosaurs striking out, standing high off the ground on their two back legs whipping each other with their tails, hissing is one more male characteristic.
Beard Display This is where the Dragons get their name, this defensive behavior is held primarily by males mostly during breeding season. The throat area of the male darkens and his chest. A slight extension of the beard to a full extension followed by the opening of the mouth to show off the inner lining of the mouth. This is a cool way for the dragon to say "hey whats up hot stuff"or "back off shes mine"
Basking Behaviors Alot of people say the most dominant males take the highest perch. I haven't seen this happen, they mostly share the spots or bask on other sides of the tank. The whole reason for basking is to bring up the body temperatures and they climb to avoid high temps of the ground in the wild. When basking under a hot light or the sun dragons gape(open their mouths)to cool off. To get the right temps read my lighting&heating section...
After reading this section I hope it helps you notice why your dragons are doing what they are doing and you can appreciate them more..