When something is "worn out", it means that it's been used a lot. It probably looks old and might not work very well anymore because it's been used so much:
All I had to wear was an old worn-out pair of jeans.
We're replacing our old worn-out washing machine and dryer.
You can also say that a person is "worn out". This just means that they're really tired:
When I get home from work, I'm worn out and all I want to do is lay on the couch and watch TV.