This is a common myth. Working out by itself does not stunt your growth.
Basically, this myth came about because, when lifting weights, it is possible (however unlikely) that you can injure your growth plates. If you injure your growth plates, they can fuse themselves prematurely and that bone will stop growing. The thing is, you can injure you growth plates pretty much any way you can break/impact a bone (sports, etc.). Just learn how to lift with proper form, don't be an idiot in the gym, and you'll be okay.
I've also heard that the extra muscle mass from lifting creates resistance to your bones growing, and your growth plates basically give up and fuse themselves prematurely. This is absolute nonsense.