Alright kiddo, imagine you are in a playground with your friends, and one day a new kid comes and starts saying mean things about your games and your friends. You might not like it and want to stop them from ruining your fun.
In China, a long time ago, some people in the government also felt like there were some bad kids who were saying and doing things that were not good for the country. These kids were called "rightists", which means they believed in ideas that did not align with the government's vision.
So, the government decided to start a campaign to stop them from spreading those ideas. They wanted to make sure that everyone was on the same page, and anyone who disagreed with them was stopped.
Just like how you and your friends might have rules in your playground to make sure everyone is happy and safe, the Chinese government wanted to enforce their own rules to make sure everyone was following the same beliefs and ideas.
However, some people thought that this campaign went too far and that the government was being too strict. They felt like it was not fair to punish people just because they had different opinions. And just like how you might not like it if someone is too strict with the rules in your playground, some people in China did not like how strict the government was being.
Overall, the anti-rightist campaign was a time when the Chinese government wanted to make sure that everyone was following the same ideas and beliefs, and anyone who was found to be opposing the government's views was punished.