The nutria is a very large aquatic rodent, introduced from South America into the American South for the fur trade. Once introduced it began to escape and spread, causing ecological damage as it went. It's an omnivore that ruins native aquatic plant beds and feasts on native crustaceans. In its own environment it serves as food for anacondas and caimans, but north of the Carolinas there's nothing remotely like these predators to keep it in check. It's been a problem from New Orleans to the Chesapeake Bay for years, and now it's spread past the Mason-Dixon line to the country's most densely populated state. (Feral nutria populations also exist in spots in the Pacific Northwest.)
In appearance, the nutria resembles a giant muskrat, but with a round, ratlike tail instead of the muskrat's rudderlike vertically flattened tail. They are not related to muskrats or beaver, but are in the rodent suborder that includes capybara and guinea pigs. Despite the deliberately alarming headline, they are also not closely related to rats:
GIANT RATS INVADE NEW JERSEY!
Animal Diversity Web entry on Nutria.