This is an expression that means "Think positively." People use this expression when they're talking to someone who's having a problem. After saying "Look on the bright side", the speaker then says something good that the person who's having the problem can be happy about. Here are some other examples of things that you could say to someone who lost his or her job:
Look on the bright side. At least you won't have to wake up early to go to work now.
Look on the bright side. You're young, you've got a good degree. I'm sure you'll have a new job in no time.