Unitatis Redintegratio is a fancy way of saying "Restoring Unity". It's something that the Catholic Church made back in the 1960s so that they could be friends with other Christian churches.
It's like when you have an argument with your friend and you don't talk to them for a while. But then you realize that being friends is more important than being right, so you make up and become friends again.
The Catholic Church wanted to make up with other Christian churches because they realized that they all believe in Jesus and that's really important. They said that everyone who believes in Jesus is part of the same big group, but they just have some different ways of doing things.
So, Unitatis Redintegratio was made to help the Catholic Church and other Christian churches work together and be friends again.