Obama joins the ranks of former presidents Theodore Roosevelt, Woodrow Wilson, and Jimmy Carter. Neither was particularly peaceful when president (although Jimmy Carter is doing a lot to make Americans forget any policies of war he had during his presidency).
Roosevelt heard his for his successful mediation of the end of the Russo-Japanese War. Wilson earned his for founding the League of Nations. Carter earned his for working to find peaceful solutions to international conflicts. And, as reported, Obama won his award for working to strengthen international diplomacy and cooperation between peoples.
Each award given to U.S. presidents has something in common --- it was given to presidents who worked to end wars or conflicts.
Presidents awarded peace prizes were given these awards regardless of how much they had to do with making the violence of the war or conflict increase. What mattered was that they looked at what had been happening and decided enough was enough---it's time to make an agreement to end this war.