To break is to abort the execution of a sentence, without killing the process.
In jconsole and the web version hitting ctrl-c while a sentence executes sends the break signal. Hitting ctrl-c in jconsole while no sentence executes, terminates the process.
To break from a different session, for example when the target session
became unresponsive, the target session needs to have a so called
breakfile in jpath '~user/break' (check whether one appears there when
staring the session).
If no breakfile exists, it can be created (obviously only before the
session hangs) by running setbreak 'foo' in the relevant session,
which tags the session as "foo".
Then, abort the running sentence in this session by calling break 'foo' from another J session. By default JQt creates a breakfile
"default" which can be triggered without having to name it (break '').
Jconsole sessions do not have a breakfile by default.
In my experience it might be necessary to send the break signal repeatedly sometimes (regardless of whether ctrl-c or a break-file is used).