The time when you are depressed and are thinking about what ever pops into your mind. Time moves slow and you are in a daze. The time when you feel like you're just broken, and need time to repair.
You just broke up with your girlfriend, and now you're just sitting in your room on your bed just thinking, now that is blue time.
That 30 minutes or so just before sunrise when everything in the world has a blue tinge to it. Usually noted to point out the fact that you've been up all night.
"How late did you guys stay up last night?"
"Oh, it was blue time when everyone went home."