Historically watch calibers were designated by size. The French system for measuring sizes is the ligne. A ligne is equal to 1/12th of an 18th century French inch. The american system is simply “size.” In the American size the 0 size measures 1 5/30 inches and each size larger or smaller is 1/30 inch different. For more on sizes check out this article on Timezone.
The ligne gauge is a simple graduated piece of metal for determining the size of a watch caliber. To use the tool you place it across the dial side of the mainplate and read the size from the gauge. Size is really important, especially with older European movements or American pocket watches.
Simple tool, but indispensable.