To understand why Obama won the prize, you need to understand about the history of the prize. The prizes were created because Nobel was upset that his invention of TNT caused so much destruction in the world. At the time, TNT was a WMD.

Obama's worked to reduce nuclear weapons while in the US Senate. That effort would've made Nobel proud.

Further, Obama recently removed Syria's declared chemical weapon stock pile. If he didn't earn it before this, he definitely earned it now. This is directly at the heart of why the Nobel prize was created.

http://en.wikipedia.org/wiki/Nobel_Prize

In 1888, Nobel was astonished to read his own obituary, titled The merchant of death is dead, in a French newspaper. As it was Alfred's brother Ludvig who had died, the obituary was eight years premature. The article disconcerted Nobel and made him apprehensive about how he would be remembered. This inspired him to change his will.