If you've played Fallout 3, then the simplest description of Fallout: New Vegas is that it is more of the same goodness, but with RPG enhancements including a better companion management system, Hardcore mode which places greater emphasis on strategy and realism, and a Reputation System that means your actions now have more consequences.
In terms of genre, Fallout: New Vegas can best be described as a cross between an adventure game, a role-playing game, and a first person shooter, having elements of all three. Fallout: New Vegas begins in the late 23rd century, shortly after the events of Fallout 3, allowing you to once again enter this bizarre alternate reality and explore the post-apocalyptic wasteland surrounding and including Las Vegas, now known as New Vegas. If you're unfamiliar with the Fallout series of games, the quirky premise is that America effectively became culturally stuck in the 1950's 'Atomic Age', right up to a devastating nuclear war which occurs in the early 21st century.