Self-explanatory. Say, a part has a touched event, and two scripts are working on that part. One script has called a connection event, but the other script wants to disconnect that event. (or disconnect all other events). So you can call
Part:DisconnectAllConnections() (and disconnect all other connections associated with it).
(Keep in mind, that if you call
Instance:DisconnectAllConnections() from the client, and the connection happened in the server in Experimental Mode off, and vise versa, then it won’t work. Wasn’t that already obvious?)
(Edit: Idea not plausible. Don’t count on it.)