Catholic emancipation was when people who follow the Catholic religion were given the right to do things that were not allowed before because of their religion.
Before Catholic emancipation, Catholics were not allowed to do certain things like own land, be in Parliament (the group of people who make laws for the country), or even have certain jobs. This was because many people in the past thought that Catholics were not loyal to the country and were more loyal to the Pope (the leader of the Catholic Church).
But over time, people started to realize that Catholics were also loyal to the country and should be allowed to do the same things as everyone else. It wasn't fair to treat them differently just because of their religion.
So in 1829, the British government passed a law called the Catholic Relief Act that allowed Catholics to do things they couldn't do before. They could own land, be in Parliament, and have certain jobs like lawyers and judges.
This was a big deal for Catholics because they finally had more rights and weren't being discriminated against just because of their religion. It was a step towards treating everyone equally and with respect, no matter what religion they followed.