I guess the best analogy is a "virtual desktop" but for the terminal.
It's is a program which runs in a terminal and allows multiple other terminal programs to be run inside it.
Each program inside tmux gets its own "page" or "screen" and you can jump between them (next-screen, previous-screen etc).
So instead of having multiple terminal windows, you only have one and switch the screen/page inside it.
You can detech from the program and leave it running - so next time you log on to the server, you can re-attach to it and all your screens/sessions are still there.
Not super useful on your local machine - but when you have to connect to a remote server (or several) is really shines. Especially if you have to go through a jumphost. You can just connect to your jumphost, start tmux, then create a "screen" for each server you need to connect to - do your stuff and deattach. Next time, just re-attach and all your stuff is there.