Hi there,
with tmux you can make your life a little more easy, if you have to work on the command line or manage one or more servers. So here is what I did:
If I connect to one of my servers via ssh I'm doing this always via my ssh key. Here you can find a detailed guide on how to setup a connection via ssh by using a key and a password for the key. If you're using this kind of authentication you just have to remember one password (the one for your private key) and you can login to any server you distributed your public key to. So now you can easily connect to your server(s) without creating another password for your user on another server.
But after login you have still just one shell available but maybe you need sometimes more shells but don't want to login for it. Thats the moment when you should start tmux.
As there are already some good tutorials and explanations I don't want to make my own one here so just visit here, here, here (german) or here as a starting point.
There is also a book available about tmux. I didn't read it, but maybe useful for someone who wants to dive deeper into tmux.
Cheers.
