You’ve gotten a lot of good replies, so I’ll give you an example:
My wife and I set up a Minecraft server on an old work computer of hers. We would SSH in, start the server, and play. However, if the host lost the SSH session, the entire server would crash because the session would close.
With tmux, we could attach, start the server, and unattach. I could start the server and later my wife could attach to close it. I could SSH on my phone via iSH, attach, start the server, unattach, and close the app. We could troubleshoot mods together, since we could both see everything that happened in the session on our screens.
It offered a level of flexibility a traditional SSH session doesn’t give.