There are likely dozens of other uses for New Window (feel free to add your own below). But one of the best (you saw this coming, didn’t you?) is to edit in one window and see the final version, without selections, in the other. For example, open a new window and put it into Preview mode (press W). Then switch back to the first window and edit away. When you do your Undo/Redo (Command/Ctrl-Z, then Command/Ctrl-Shift-Z) moves, you’ll see before and after in both windows — one with the selection and one in its pure, unsullied state.