A centre for the study of professions is a place where smart grown-ups go to learn about different kinds of jobs that important grown-ups do. They want to know lots of things, like how those grown-ups learn how to do their jobs, what makes them good at it, and how they keep doing it so well.
It's like being in a big playroom with lots of toys, where the toys are different jobs and the grown-ups who do them. The students who come to the centre get to play with the toys, but they also get to ask questions about them and learn how to play with them in new and better ways.
Just like how you might practice drawing or building towers with blocks, the students at the centre for the study of professions practice asking questions, researching, and writing down what they learn. They might even get to go out and visit the grown-ups who do the jobs they're studying!
By the time they finish learning at the centre, the students will know a lot about lots of different kinds of jobs, and they might even be able to grow up and become the important grown-ups they studied!