The conversion moment with tmux is always the same. You are halfway through something long over SSH, the wifi hiccups, the connection drops, and the process dies with it. Hours gone. Then someone shows you that if you had run it inside tmux, you could have reconnected and found it exactly where you left it, still running, nothing lost. After that you never go back.
That is the whole pitch. tmux keeps your terminal session alive on the server independently of your connection to it. You start a session, do your work, detach with Ctrl-b d, and the session carries on without you. Log in from anywhere later and tmux attach drops you straight back in. The long build, the migration, the tail on a noisy log: all still there.
You can learn the rest gradually, and it is worth it, the splits and panes and windows that turn one terminal into a proper workspace. But the two commands that justify installing it on every box you touch are tmux new -s work to start a named session and tmux attach -t work to return to it. Everything else is a bonus. Those two mean a dropped connection is a shrug instead of a disaster, and that alone has paid for itself more times than I can count.