Long Island is, as the name implies, a long island. It extends east from Manhattan into the Atlantic, making maps of New York State really hard to draw (Long Island usually winds up in an awkward inset).
The western-most quarter of the island is made up of the boroughs of Brooklyn and Queens, though when referring to Long Island, most people are referring to the outermost two counties: Nassau and Suffolk (aka the suburbs). It has the dubious distinction of only being connected by road to the rest of the world via New York City, meaning that, even though Long Islanders are fiercely proud suburbanites, their sense of reality is totally mediated by the city. This must do horrible things to their psyches. Indeed, people in Connecticut would rather just pretend such a place didn't exist, and that the pristine beaches their WASP forefathers landed on faced the clean, open ocean, rather than whatever toxic runoff seeped off the coast of the island's north shore.
Long Island is accessible via the very obviously named Long Island Expressway and Long Island Rail Road, but you don't need to know that, because you should only go if you're going to visit family (and if your family is from there, we're sorry), or, if you're wealthy, to sun yourself in the Hamptons. Long Island has a tiny wine country you could visit, for some reason, on the part of the island that hasn't been completely overtaken by tract housing. Don't. It's not really worth it. And don't ever stay too long.