Display order is a way of controlling the order in which the options in a list appear. The bigger the display order number, the lower the item will display in the list. Think of it like a "weight" for each option, with heavier items moving to the bottom of the list, and lighter items floating to the top. If no display order is set (i.e. everything is 0), or several options have the same display order number, the list will revert to ordering alphabetically or numerically as appropriate.
The screenshot below shows the list of communication methods. Display order has been used to control the order of the drop-down list, with the most common method of contact (telephone) appearing at the top and the least common (letter) appearing at the bottom.