That's a dragonfly nymph's discarded exoskeleton. Dragonfly metamorphosis is simple, so the dragonfly's immature stage is somewhat anatomically similar to the adult dragonfly, only that it's smaller, wingless, and aquatic. Immature stages of insects with simple metamorphosis are referred to as nymphs.

Dragonfly nymphs breathe underwater with gills in their rectums. Moreover, a nymph can move about using jet propulsion. It draws water into its rectum through the anus, then expels it, the faster the water being expelled, the faster the nymph shoots forward.

When a dragonfly nymph is ready to metamorphose into a flying adult, it pulls itself from the water, climbs what usually turns out to be shoreline vegetation, holds on tight as its exterior skeleton, or exoskeleton, begins splitting, and finally the interior being emerges from its old "skin."

The nymph exoskeleton in the picture is encrusted with mud. Still, you can see the gaping hole in its back where the new winged dragonfly emerged. I've watched this process before and can tell you that the newly minted dragonfly is very vulnerable to predation at this moment. Its new exoskeleton is still soft, and at first its wings aren't completely unfurled. For awhile you have a soft, juicy dragonfly who can't fly away, often in plain view of predators such as bullfrogs.

Damselflies also produce aquatic nymphs, but they are more slender than dragonfly nymphs. In fact, horsefly and deerfly nymphs are aquatic, too, but they are legless, looking somewhat like slender, conspicuously segmented torpedoes tapering at both ends.