Why? It's basically making the Clintons our international face.
This is a page out of Don Corleon's book...keep you friends close and your enemies even closer.
A. It makes Clinton an official part of the Obama administration, thereby precluding her from a 2012 run against him.
B. Additionally, it fortifies his run in 2012 by securing the 18M Hillary voters who, even if they're not over their bitterness that Hillary lost by that time, will be voting to keep their girl in her high office position.
C. And to that end, it's a conciliatory move for the Democratic party.
D. If he hadn't offered her the highest cabinet position, he'd be dropping a seed of further resentment now that would metastasize into insurmountable trouble 4 years from now.
E. Even though it makes her the international representative, she is the international representative of the Obama administration. (The world leaders are very much aware of who the President is)
F. If it doesn't work, she can be fired.
Hey, gotta give the man credit. He didn't get this far by playing checkers. This guy plays chess.