Have you ever seen someone use a tiling window manager instead of a desktop environment? Where it keeps all the currently running apps on screen in evenly sized tiles so you can see everything at once, nothing is in the “background?”
Tmux is a bit like that, but only for the terminal. It allows you to open multiple terminals in one “screen” or terminal emulator window, and switch between them with keyboard shortcuts. So if you want to look at your source code, test run your source code, and watch htop to see how it performs, you can do that with Tmux. It’s a bit less cumbersome than opening three terminal windows.
It also works over SSH, so you can SSH into a server or something, start tmux, then easily run several tools simultaneously.
Tmux sessions are also persistent. Imagine if you were in the middle of working on something on your desktop at the office, then it’s time to go home. You can detach your session, SSH into the box from your laptop, reattach that session and keep working right where you left off.
If you work in the terminal a lot, it’s a handy tool.