Censoring in statistics is like when you want to measure how long it takes to finish eating a big pile of cookies, but you only get to see some of the people who finish eating all the cookies.
Let's say you want to know how long it takes for all the people to finish eating the cookies, but some people leave before finishing the cookies. This is called right-censoring. It's like you don't get to see how long it takes for those people to finish eating the cookies, so you have to pretend as if they never started eating them in the first place.
On the other hand, you might be curious about how long it takes for people to start eating the cookies, but you only observe some people after they've already started eating them. This is called left-censoring. It's like you don't know exactly when those people started eating the cookies, only that they had already started when you began to watch.
In either case, the information you have is incomplete, and you can't simply ignore it. Instead, statisticians use a special technique to estimate what might have happened to the data that you don't have. It's kind of like guessing based on what you know, but it requires lots of special math and calculations to get it right.