The Alto created the image from a display list, like the Atari 800 or the Amiga. So you could have a wider rectangle on most of the screen for pictures and a narrower rectangle at the bottom for displaying status. It was not up to showing overlapping windows. Nearly all applications just set things to one rectangle, having a frame buffer in practice. This was the case for Smalltalk, which is where Bill saw the overlapping windows. One problem is that filling up the whole screen (606x808) used up half of the memory and slowed down user code, so Smalltalk-72 reduced this to 512x684 to get back some memory and performance.

The Smalltalk-76 MVC user interface that the Apple people saw only ever updated the topmost window which, by definition, was not clipped by any other window. If you brought some other window to the front it would only then be updated. But since nothing ran in the background it was easy to get the wrong impression that the partially visible windows were being handled.

Bill's solution had two parts: one was regions, as several other people have explained. It allowed drawing to a background window even while clipping to any overlapping windows that are closer. But the second was PICTs, where applications did not directly draw to their windows but instead created a structure (could be a file) with a list of drawing commands which was then passed to the operating system for the actual drawing. You could do something like "open PICT, fill background with grey pattern, draw white oval, draw black rectangle, close PICT". Now if the window was moved the OS could recalculate all the regions of the new configuration and re-execute all the PICTs to update any newly exposed areas. If the application chose to instead draw its own pixels (a game, for example) then the OS would insert a warning into the app's event queue that it should fix its window contents.

In parallel with Bill's work (perhaps a little before it) we had Rob Pike's Blit terminal (commercially released in 1982) which added windows to Unix machines. It had the equivalent of regions (less compact, however) but used a per window buffer so the terminal would have where to copy newly exposed pixels from.