It's called honeydew, and it's secreted by aphids. If you check the bottoms of some of the leaves, you may see small greenish insects. Leaves may also have light green/yellow areas where the insect has fed. The black growth is called sooty mold, a fungus that lives on honeydew. Controlling the aphids will control the sooty mold. Using insecticidal soap or horticultural oil will help control them, however bad infestations often need chemical control.

BTW, the proper common name for trees and shrubs in the Lagerstroemia genus is Crape Myrtle.