Okay kiddo, so a "centre" means a place where people do research and learn about something. In this case, the "Centre for the Study of the Legacies of British Slavery" is a place where grown-ups study and learn about something that happened a long time ago in England called "slavery".
Slavery meant that some people would treat other people very badly, like they were not actually people but things that you could own and make do work for you. It was a very bad thing, and it happened a long time ago in England.
Now, this "centre" is studying and learning about what happened during slavery and how it affects people today. There are a lot of ways that slavery still affects people today, even though it happened a long time ago. The people who work at this centre want to learn about those things so they can help make things better.
So, that's what the "Centre for the Study of the Legacies of British Slavery" is all about - it's a place where grown-ups go to learn about something bad that happened a long time ago and how it still affects people today.