Okay kiddo, have you ever promised to do something and later denied that you ever made that promise? Non-repudiation is a way of making it impossible for someone to deny that they did something.
For example, let's say you wrote a note to your friend and gave it to them. Non-repudiation means that you can't later say that you never wrote that note, because there is proof that you did. The note itself and maybe even witnesses who saw you write it, are evidence that you can't deny.
In the grown-up world, non-repudiation is very important when it comes to legal matters and digital communication. If you send an email or sign a digital contract, you can't later deny that you sent it or signed it, because there is a digital trail that proves you did.
People use things like passwords, digital signatures, and encryption keys to provide non-repudiation. It basically makes it so that when you do something, you can't deny that you did it later on.