Use position:absolute; and set the “popup” one to be positioned within the boundaries of the other. The “popup” div should likely also be smaller.
Use z-index to stack the “popup” one above the other one (give it a higher value for z-index).
If you want to make it look like the inner div is really floating above the other one, create a shadow with something like border-right:2px solid black and border-bottom:2px solid black.
If you want to make it actually pop up/appear/disappear, you will need to use some script.