This is something like a TV or film producer, but for live performances, like plays, concerts, or operas.
Why I Looked It Up
In an article about the current chess grand master Magnus Carlsen, said this:
[Magnus Carlsen] has also done something that none of his contemporaries or predecessors, not even Garry Kasparov, who held the world title from 1985 to 2000, managed to do: He has leveraged his fame to become one of the chess world’s leading impresarios.
The point being made is that Carlsen now has a lot of business interests involving chess. The article went on to describe all of Carlson’s business interests. There wasn’t a lot of “producing” along the lines of the traditional definition on impresario, but there are lots of business interests around chess. So, he’s making money from a performance sport, which I suppose is sort of related?