I can’t tell you where this expression comes from, but it refers to someone being happy, refreshed, and ready to take on the world after a good night’s sleep.

e.g. The baby finally slept through the night, and I woke up bright-eyed and bushy-tailed.

This expression, however, is often used ironically, particularly to refer to someone who looks rough after a poor night’s sleep or pulling an all-nighter and staying awake all night.