Why is 'speech-dispatcher' listed so many times in sound settings and what is it?

You have enabled the ScreenReader in GNOME, that's all. To disable the Screen Reader start Universal Access and click Screen Reader.

You can see four entries in Sound, because there are four processes

% ps xa | grep -P 'speech-dispatcher.*\.conf'
14520 tty2     Sl+    0:00 /usr/lib/speech-dispatcher-modules/sd_generic /etc/speech-dispatcher/modules/generic.conf
14523 tty2     Sl+    0:00 /usr/lib/speech-dispatcher-modules/sd_cicero /etc/speech-dispatcher/modules/cicero.conf
14527 tty2     Sl+    0:03 /usr/lib/speech-dispatcher-modules/sd_espeak /etc/speech-dispatcher/modules/espeak.conf
14532 tty2     Sl+    0:00 /usr/lib/speech-dispatcher-modules/sd_dummy /etc/speech-dispatcher/modules/dummy.conf

Sometimes the processes, however, seem to be not properly terminated after the Screen Reader was terminated. Therefore:

killall speech-dispatcher

As said here, it is a known upstream bug which is currently being worked on.

In my setup, most of the GNOME stuff is not used and in the gnome-control-center there were a lot of speech-dispatcher processes as well. I hadn't the Screen Reader enabled.

But still, the processes were there. I had to disable the service using systemd tools:

sudo systemctl disable speech-dispatcher  # disables systemd service

And kill the remaining processes after that like in the accepted solution:

killall speech-dispatcher