The nymphs of periodical cicadas live underground, sucking on tree roots, for 13 years, until they emerge. They leave their shells behind as adults, and crawl into trees to find a mate. That's what all the buzzing or singing is about. Males trying to find their lady love.
Periodical cicadas have been around a long time, maybe even as far back as when the glaciers melted. And while birds love to snack on them, there is no predator that thrives in the great numbers, with an identical lifecycle to these cicadas. That is why they've survived so long.