The display of male agama lizards is to attract female lizards for mating. Agama lizards are known for their bright, colorful displays, which they use to show off to potential mates. The display typically involves the male standing up on his hind legs, puffing out his throat, and waving his tail. This display is meant to demonstrate the male's strength and vitality, and to attract the attention of female lizards who are looking for a suitable mate.
It is important to note that the display of agama lizards is not meant to scare predators or regulate body temperature, although it may have these side effects. The primary purpose of the display is to attract a mate and increase the chances of successful reproduction.