Extinction is like when you stop giving attention to someone or something when they do something you don't like. Let's say your little sister is always nagging you to play with her, but you don't want to. If you ignore her every time she asks, eventually she will stop asking because she learns that nagging doesn't work anymore.
In psychology, extinction works the same way. It's when you stop rewarding or punishing a certain behavior, so the behavior stops happening. For example, if you have a dog that jumps on people when they come over, you might try to stop the behavior by yelling at the dog or pushing it off. But if you stop giving it attention or treats when it jumps, eventually the dog will learn that jumping doesn't get it anything good, and it will stop doing it.
Extinction is important because it can help get rid of unwanted behaviors without resorting to punishment or negative reinforcement. It can take time and patience, but ultimately it can lead to better behavior in animals and people alike.