Comes from the 1989 film "Weekend at Bernie's"
It's when you fall asleep sitting in a chair of some sort i.e. desk or couch with sunglasses on. The best ways to pull a Bernie are to stay loose and fall asleep with some sort of neutral grin.
The career-furthering act of forming an amazing new band which will hopefully match or surpass the band from which you have for whatever reason left. Can also be used to describe forming a side project which makes your usual band look sucky. Named for Steve "Beanie" Hewitt who is one person notable for this stunt.