For you junkies who just have to know why...
Eighteenth Century European armies used cords and aguilettes to distinguish service branches and officers from enlisted. Many Continental Army units adopted this custom. After the American Revolution, cords fell into disuse until the Mexican War. During this war some Mexican military leaders threatened to hang any captured U.S. Officers. Many gallant men defiantly wore short ropes on their shoulders as they pressed home the attack in mocking tribute to their enemy's empty threat. Cords and aguilettes soon officially reappeared to denote various positions and awards and have remained with our Army until this day
General Washington selected the color blue to distinguish his tough and resolute infantry in the Continental Army from other types of soldiers. General LaFayette chose a light blue color to outfit his American Infantry Corps. For the next 120 years, the official Infantry color alternated between blue and white until 1904 when the Army officially adopted what we now know as "Infantry Blue."
In 1951, the Army leadership sought to encourage and recognize foot soldiers who were bravely fighting intense battles in Korea. They soon adopted the Infantry Blue Cord. This cord would only be worn by fully qualified Infantrymen and would announce for all to see that these men would be on the front line when our nation was at war.
Today, enlisted graduates of Infantry Basic Training receive their blue cord at the end of their final FTX. Graduates of the Infantry Officer Basic Course complete their weeklong final FTX and after road marching back to building 76 have their blue cords pinned on them by their platoon trainer NCOs. The SSG or SFC who pins on the blue cord then renders an honorary salute in symbolic recognition of their welcoming the Lieutenant into the ranks of the Infantry.
http://www.benning.army.mil/iobc/cad..._blue_cord.htm