What are these webs on my crape myrtle?

This is likely spider mites. In heavy infestations the small insects produce a webbing around them. Currently, it is the end of the growing season so there is no need to treat, however break up the webbing to expose the spider mites to predators.

Related Videos:
Identifying Spider Mites
Crape Myrtles
Treating Crape Myrtle Bark Scale
Pruning (Not Murdering) Crape Myrtles

Related Resources:
Crape Myrtle Diseases & Insect Pests
Spider Mites