If you are running tmux locally it would allow you to do things like kill X, log back in, open a new xterm, then pick up where you left off. The session isn't paused or suspended, it continues running the entire time even though the gui terminal emulator died.

If you are running tmux remotely, then it lets you start working at home on your laptop (over ssh), close your laptop, drive across town, turn your laptop back on, ssh back in, and pick up where you left off.

The way I use this at work is I have many long-running tmux sessions running on my desktop (one for each 'project', and one for a few interactive db sessions and the like). I then work over ssh with a fullscreened Putty instance. When I want to switch projects I can just hit C-b s then select the session I want to switch to.

At home I use a laptop with linux (and the Awesome WM (similar to xmonad, though less hardcore I suppose)) but most of my 'work sessions' are on various other machines. I ssh into them and connect to the correct session with tmux. Since Awesome lets me arrange windows with tags I do that a lot for work sessions (like tagging a few terminals and a browser window that has docs opened in it) but I consider those to be more ephemeral. I close them out when I start running low on resources (memory, cpu, battery, etc) but the tmux sessions live on (local or remotely).

(I use to use straight up xterm as well, but switched to urxvt because my new laptop has a high DPI screen that makes urxvt's nicer font rendering support sort of necessary.)