The D60 is a refresh of the D40x. The things that changed between the two cameras:
Image quality improvements. The D60 uses the EXPEED processing system, and as such it has some very modest image quality improvements, most of which don't really show up until you bump the ISO way up and pixel peep. Still, as good as the D40x was, any improvement is always welcome. The D60 seems to be a little cleaner in its images, and that's a worthy improvement.
Sensor cleaning. The D60 gets the shake-it-and-drop-it sensor cleaning that its big brothers have (D90, D300, D700), but with a twist: the airflow caused by the mirror flipping back and forth has been tuned so as to help remove dust from the sensor area. The airflow bit is, in my estimation, untestable and thus very modest at best, but the sensor cleaning function is welcome and really needs to be on this class of camera, where the user is less likely to want to open it up and do manual cleaning.
Viewfinder changes. The D60 knows when you've put your eye to the viewfinder and turns off the color LCD, removing an annoyance many had with the D40 and D40x. Oh, and the interface on that color LCD now rotates with the camera. The viewfinder also provides confirmation of focus for manual focus users.
Minor menu changes. Nikon has added a stop motion movie function, in-camera raw processing, and some additional RETOUCH menu gimics (cross star and color intensification).
Dedicated Active D-Lighting button. You can now turn Active D-Lighting on and off without dropping down into the menus.
All these changes are welcome, though none of them are earthshattering. The bottom line on the basic feature set changes is that if you liked the D40 or D40x, you'll probably like the D60 a little more.