Bright Man is one of the many robot masters created by Dr. Cossack. Supposedly extremely intelligent but extremely nerdy, going on literally for days about the history of electricity.
Of course, since people never listen to his lectures, he freezes their bodies in time to make them listen.
Dr. Cossack used him as a tool to lure Megaman away from the real threat, Dr. Wily, and ultimately get his daughter Kalinka back. Bright Man had stored several books in a seperate conpartment in his boss room. The player, who would most likely find that ridiculous, dismissed this fact during Mega Man 4.
A couple years later, during Mega Man IV, another robot that imitated Bright Man (most likely Dark Man II.5) attacked an electricity plant. Bright Man had noticed, and soon after the defeat of this Robot Master he fixed everything up and subsequently foiled Ballade's dark-room-with-spikes trap by accident.
Between 20XX and 21XX, Bright Man had seemingly short-fused and became disabled entirely. It seems he overslept while recharging, which caused his power supply to explode. His few remaining parts (a light bulb and three screws) then went on display at the International Museum of Robotics.
"Hello, Megaman. How do you do?" (Mega Man 4)
"Oh, you mean Flash Man? No, I'm nothing like THAT loser. I can still move after freezing time, y'know!"
"Hm, what does this switch do?"
"Oh... sorry Megaman."
"Wait, I didn't mean to cause you loss of life! No, seriously, ProtomaAAAAAAAAAAAAAA"