The most common use case for tmux is to put long running terminal apps in the background when working remotely, e.g.:
<pre style="background-color:#ffffff;">
<span style="color:#323232;"># start a new virtual terminal
</span><span style="color:#323232;">tmux
</span><span style="color:#323232;">
</span><span style="color:#323232;"># do something in the terminal that will take a long while to complete
</span><span style="color:#323232;">sleep 1m
</span><span style="color:#323232;">
</span><span style="color:#323232;"># put the virtual terminal into the background
</span><span style="color:#323232;">Ctrl-b d
</span><span style="color:#323232;">
</span><span style="color:#323232;"># do other stuff
</span><span style="color:#323232;">
</span><span style="color:#323232;"># reattach to the virtual terminal
</span><span style="color:#323232;">tmux a
</span>
This allows you to disconnect from the server, but keep the process running in the background. It can also do split screen with multiple terminals, provide a scroll back buffer (Ctrl-b PageUp) and other stuff. But using it for background processes is probably the most common one.