A bouquet of tiny arches? A miniature cave system?
Known as honeycomb weathering or "swiss-cheese rock," tafoni (singular: tafone) are small, rounded, smooth-edged openings in a rock surface, most often found in arid or semi-arid deserts. They can occur in clusters looking much like a sponge and are nearly always on a vertical or inclined face protected from surface runoff.
At Arches, tafoni are most often found in the Entrada and Navajo sandstones, both of which are made of sand from ancient dunes cemented together by calcite (calcium carbonate, CaCO3), which is soluble in water. Moisture wicks through the porous rock, dissolving the calcite and then depositing it as crystals at the surface when it evaporates. Tafoni shows this process on overdrive: accelerated, focused weathering of pockets of rock with slightly hardened bands in between. What results is an intricate, lacy structure that often resembles a honeycomb.
In other places, you might see a straight line of holes in the rock. There, water has dissolved pockets of less-well-bonded sandstone, often at the contact between two rock layers. Tapping a rock surface will sometimes result in a "hollow" sound, indicating the presence of pockets within.