On set editing is the dream. I have yet to have the chance to do it, but I would jump at the opportunity. This means taking dailies straight from the camera and editing quickly to show the director what is and isn't working. If you'd like to chat more about this, I am on board!
The DIT role differs from set to set. Generally, I take the memory cards from the DP, copy and transcode the dailies onto the harddrives and prepare the dailies for the assistant editor.