One use case is a new message indicator. Unlike icons on the desktop, keyboard lights are visible even when a full-screen application is running, or when we're to the side of or across the room from the computer, or when the display is asleep. I depend on this for my daily communications.

Another use case is for keyboard macro utilities to indicate the state of layers, modifier modes, or multi-keystroke input sequences.

I expect that others exist, since hardware lights can indicate just about anything, and are especially valuable where visibility is important. Even shell scripts can use them on X11, via the xset command.