The old Kinect was notorious for needing a fairly large space in which to play, so the camera could accurately capture your movements. I mean, I live in a house, and my living room setup wasn't big enough.
The new Kinect, packing a wide-angle lens, is supposed to alleviate that problem, but it's not like it's perfect. You'll still need to clear an optimal amount of space. How much? Here's the official word from Microsoft:
Single player about 4 ft. 7 in. (1.4 m) from sensor. Two players about 6 ft. (1.8m) from sensor. Play space will vary by game, application, sensor placement, and other factors.
That's a big improvement over the original, which needed 6-8ft just for singleplayer.