Which display?

The anole can display it's dewlap for two reasons;

Firstly, it can be territorial to warn off other anoles that they have entered his home range. Secondly, it's used to recognize a particular anole species and in selecting partners. Females may chose mates with the best-developed dewlap!

There was a second anole close by on the fence but I didn't hang about to see if this was a territorial or mating display :)