Aside from tabs/panes/persistence already mentioned, it serves as a portable, programmable layer that will work anywhere, whether on the client or server side. I set up my key bindings once and now they work over SSH from Windows, local terminal emulator, on a Linux framebuffer console or even through a serial port. While I do use a tiling/tabbing window manager, tmux is just really good at what it does so I still keep using it for my terminals.