My echo keeps showing this indicator. It goes on for a long while, stops some time later, but then I notice it's happening again.
Cyan on blue
What it means:
A cyan spotlight on a blue ring means that Alexa is listening.
The light ring glimmers briefly when Alexa has heard and is processing your request. A briefly glimmering blue light might also mean the device is receiving a software update.
Check the link for a complete description of different led patterns: