If you properly set up the Blink Mini according to the instructions, this is one of the stages the camera will go through when it re-connects if you disconnect it from the power. When you plug it back in the light will first show or flash red – indicating a connection issue – then it will turn blue, then blink green for a while as the connection is made to your wi-fi and then to the internet. You can check this by looking at the camera in your Blink app.
The green light also appears when the microphone is being accessed remotely in real time (so it might mean someone else in your household with the app is listening to you). Some solutions: