The term overlay comes from the world of architecture and drafting, where a clear plastic layer of extra information is superimposed on top of an architectural diagram. The overlay shows specific features such as positions of trees, easements, or heritage information. That extra information can be distracting and so is left off the main diagram until it's needed.
In the world of computing, the term overlay is popularly used in the design of character-based user interfaces. Even an 80x24 character display is big enough to support forms and menus, and that's still done today. A character-based overlay uses the rigid 80x24 or 80x25 display to put fragments of extra text on top of the basic screen as required. A common use of character overlays is to provide interactive help. That help "paints over" part of a data-entry screen with new information when the user presses F1. Another use is to expose a menu bar across the top of the screen when the user presses Esc. In both cases, the overlay contains partial screen information only.
Now that we have XML-based GUIs such as HTML and XUL, the term overlay is reappearing again. XML overlays are not layered like the earlier technologies, though; instead, they're merged.