The phrase "fun and games" is used in a few other expressions as well. When they're used together like this, it's usually meant to criticize the idea of people doing things that aren't careful or serious enough. For example, you can say this to some children who are playing too roughly:
It's all fun and games until somebody gets hurt.
You can say this if someone invites you to do something fun but you're busy and stressed out:
I appreciate the offer, but I don't have time for fun and games. I have work to do.
This last example would sound a little rude, though.