What do periodic Cicadas do in the ground for 13-17 years before emerging to mate?

These insects are related to aphids. Like aphids, they use large population sizes to overcome predation. All the adults emerge together and this is more food than the predators can eat at once. It allows many of the cicadas to breed successfully. The reason some cicadas only emerge once every 17 years is it discourages predators from becoming cicada specialists. Its annual relative is host to a large parasitic wasp. The wasp preys only on this species of cicada. The wasp survives because it has a reliable source of food every year. The 17 and 13 year species of cicadas don't have predators which target them specifically.