Items in your menu will be displayed from left-to-right, top-to-bottom, always. The order in which they appear is defined by their same order in the Backend configuration.
The live menu, with items Blue, Green Yellow and Red in order.
The backend menu, with the same order applied.
If the order on the backend is changed, the same change will be applied on the live menu. To change order, you can click Move/Delete on the top bar. The icons will animate. You can then click and drag the icons to change their order.
After making the changes be sure to hit Save on the top bar to commit the changes. The new menu will be instantly available.