I get more email on this operation than anything else to do with my Rubik's cube solution. This is a more detailed explanation. First let me reprint one version of the operation for reference:
If the two cubelets are on adjacent edges, hold them at UF and UR and do:R- D2- R* D2* R- U- R D2* R* D2 R U
It helps to break the operation down into logical parts:
1. {R- D2-} I think of this as "move the UR cubelet down into the middle slab, and slide it sideways out from in between the two corners that surround it (the 'corner-mates')".
2. {R* D2*} "Move the corner-mates around to the back, then move the UR cubelet all the way around the cube, back in between them." The result of doing this is that the cubelet has been straightened out (flipped) with respect to its corner-mates.
3. {R-} "Put the UR cubelet, and its corner-mates, back up on top where they belong."
Now this UR cubelet is happy, but mass destruction has been caused on the layers below. The remaining moves (or just step 5, depending on your perspective) do basically the same stuff in reverse, with a different top cubelet, accomplishing two things: 1) this other top cubelet is flipped; 2) all the mayhem below is fixed.
4. {U-} "Move a different top cubelet into place."
5. {R D2* R* D2 R} "Exact reverse of steps 3, 2, 1."
6. {U} "Reverse of step 4."
Note that the only difference between the two options for this move in my solution are steps 4 and 6 here -- the ones that determine which cubelet along with UR will be flipped.