This arch, in Arches National Park in Utah, formed by erosion of solid rock. Water is the sculptor, even in deserts like the high Colorado Plateau. (more below)
Rainfall acts in two ways to erode rock into an arch. First, rainwater is a very mild acid, and in rocks with a calcite cement between its mineral grains, that cement slowly dissolves. A shaded area or a crack, where water lingers, tends to erode faster. Second, water expands as it freezes, so wherever water is trapped it exerts a powerful force upon freezing. It's a safe guess that this second force did most of the work on this arch. But in other parts of the world, particularly in limestone regions, dissolution creates arches.
Another kind of natural arch is a sea arch.