The Cauchy-Crofton Formulae describe a way to calculate the length of a curve (of any type, it doesn't need to be regular, nor close or continuous). To do so, me need to measure the intersections of the curve with the (infinite) set of all straight lines.
Of course, in reality, this can not be done. But we can still try to approximate the length of the curve with a few lines. It turns out that this approximations works quite well. This is especially useful for nasty curves, that we don't have formulae to systematically calculate the length.