simplyharsh has the proper answer, but I'd like to expand on it a bit:
The basics of a draggable div aren't too complicated. You attach an onclick handler to initiate the dragging. Internally, that's accomplished by changing the div's CSS so it's position: absolute. Then you start monitoring mouse movements (basically onmousemove) and changing the div's top and left according to the movements you've captured.
Dropping is a bit more complicated. You can always just release the mouse and leave the div wherever you ended up moving it, but that leaves it absolutely positioned and therefore outside of normal document flow. But dropping it "inside" some other element means a lot of prep work.
Because of how mouseover/mouseout/mouseenter events work, they WON'T work while you're dragging an element - you've got your draggable div under the mouse at all times, so there's no mouseenter/leave events being fired on the rest of the page. jquery/mootools and the like work around it letting you specify drop zones. The locations/sizes of these zones are precalculated and as you're dragging. Then, as you're dragging, the dragged object's position is compared to these precalculated drop zone locations for every move event. If you "enter" one of those zones, then internally the libraries fire their mouseenter/mouseleave/mouseover events to simulate an actual mouseenter/leave/over event having occured.
If you drop inside a zone, the div gets attached as a child of that zone. If you drop outside, then it will usually "snap back" to where it was when you initiated the drag.
Resizing is somewhat similar, except you're adjusting height and width instead of top and left.