What does the blue radius mean?
The Blue radius is the noise of your footsteps, your character's voice, or weapons. It shows the radius of the sound travel. If a character that can detect you is in that radius you will be caught.
The blue radius also seems to appear when you are out in the open doing something naughty. For example, assaulting a passer-by or breaking into a car.
I thought it to be an indicator that passing cops might take more notice of you.