Better graphics, larger memory + hard drive, more social features like the ability to record gameplay footage and send it to friends, better processor, much more extra features like the ability to use your Xbox one as a DVR, etc. Most importantly though Xbox one will be able to support much bigger, much more powerful games that could not be created for Xbox 360. For better details, check out: http://www.digitaltrends.com/gaming/xbox-one-vs-xbox-360-spec-showdown/
well a lot really, current systems only run just under 1GB of memory for game graphics and content, next gens are going to be running (8GB on PS3 and 7GB on Xbox One, to which means they can put more into the games, including content, better/more people for multi-player, cause current gens only let up to 6 on like CODs, but now its something like you can now have 20 at a time, basically they will run smoother graphics and pretty much get rid of load times
For starters, the Xbox 360 used a triple-core Xenos processor, which was great at the time of release, but the Xbox One uses an eight-core AMD processor, which is just awe-inspiring. Secondly, Kinect was optional on the Xbox 360, but it is mandatory in the Xbox One. The Xbox One also comes with cloud storage options, which wasn't available in the Xbox 360.