Purple dot near app which downloaded by iCloud sync
A blue dot before an apps' icon name means that it has not bee run yet (or it is a new version that has not been run).

An orange dot means that the app was downloaded as a beta as installed through Testflight.

The last is from this SO answer which also suggests the colours alter if on a different background.

Try a plain black or white background to see if the colour changes to one of these known ones.