Good question !
Controllers allow to “program” a brush’s behavior using blocks.
The block system was made with a single output to ease its use and so that users don’t get lost by the node/link paradigm usually seen in 3D modeling software.
There is already a video tutorial explaining usage of the Controller system available here
Your question, though, asks for a more detailed answer, and a new video tutorial that would explain thoroughly the way it works is a very good idea indeed !