The rectangular areas of the image which need to be redrawn. Providing rectangles rather than just redrawing the whole image potentially saving a lot of effort.
The rectangles are usually supplied by the window system software when it 'calls back' asking the application to redraw or repaint itself.
This might occur because the application has spotted the data it is drawing has changed and so needs to be redrawn in which case it typically asks the window system to schedule a repaint. The repaint might also be triggered by the window system itself spotting that a window has been moved exposing a new area of the image to be drawn.
Back when working on the EuphoriaUserInterfaceManagementSystem?, we called these DirtyRectangles (if memory serves). -- DavidSaff