As explained in How it works, mu4e communicates with its
backend (mu server) by sending commands and receiving responses
(s-expressions).
For debugging purposes, it can be very useful to see this data. For
this reason, mu4e can log all these messages. Note that the
‘protocol’ is documented to some extent in the mu-server manpage.
You can enable (and disable) logging with M-x
mu4e-toggle-logging. The log-buffer is called *mu4e-log*, and in
the The main view, The headers view and The message view,
there’s a keybinding $ that takes you there. You can quit it by
pressing q.
Logging can be a bit resource-intensive, so you may not want to leave
it on all the time. By default, the log only maintains the most recent
1200 lines. mu itself keeps a log as well, you can find it in
<MUHOME>/mu.log, on Unix typically ~/.cache/mu/mu.log.