New Game+ is the name (or one of the names) of the game feature that lets the player restart a game while retaining some of the stuff earned in a previously finished game save, like experience, skills, money, weapons...
Usually found in games that otherwise have poor replayability, a New Game+ feature allows you to replay the game from the start with (almost) everything you've earned in you previous play-through, making this play-through easier.
So... Going through the same events again, with less challenge? That sounds a bit pointless, doesn't it? Well, that's only if the second play-through has not been designed properly. Ideally, in a New Game+, you should be able to use the skills and weapons you didn't have the first time to reach new areas, or fight enemies in a different way. If you have branching story lines, the player can also use the knowledge of the first play-through to answer his/her "what if ?" questions.
I'm not a big fan of that feature, as it's usually a lazy and artificial way of giving replayability to the game. Unless it's really thought through the entire level design process, which would obviously require about twice more work and time (read budget).