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 Main view, Headers view and 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 this it in <MUHOME>/log/mu.log, typically ~/.mu/log/mu.log.