The current generation of amateur drones are compact collections of sophisticated subsystems; usually at least a CPU, GPS, IMU, sonar and barometer. They typically have multiple modes of operation: manual, acrobatic, stabilized/fly-by-wire, simple, altitude hold, loiter, guided, return-to-launch, failsafe.
For a user of the drone, knowing the status of the entire system can be critical, especially if there's a malfunction. You might have a ground control station that can receive telemetry from the drone and display sensor values and subsystem status, but it's common for drones to use patterns of LED lights to communicate information to anyone who can see the vehicle. The patterns can be simple, for example green means OK, red means ERROR; or they can be complex, with a half dozen different LEDs of different colors with multiple possible flash patterns--worse than the from-zero-to-twelve beeps of the old Power On Self Test error codes.
I've collected some examples of current status LED practice in the gallery below. Make sure you check out the video of the continuously variable RGB status LED.
You might also be interested in the paper "Unlocking the Expressivity of Point Lights" for a more scientific take on the problem.