"The buck stops here" comes from the slang expression "pass the buck" meaning move the responsibility for something away from oneself to another. This originated in poker (card game) played in America, where an indicator, frequently a buck horn handled knife, was used to indicate the person whose turn it was to deal. If that player did not wish to deal he could pass the responsibility by passing the "buck," as the counter came to be called, to the next player.
American President Harry Truman placed a sign with this phrase on his White House desk. The sign was made by inmates at the Federal Reformatory at El Reno, Oklahoma. Fred M. Canfil, then United States Marshal for the Western District of Missouri and a friend of Mr. Truman, saw a similar sign while visiting the Reformatory and asked the Warden if a sign like it could be made for the President. The painted glass sign on a wooden base has the words "I'm From Missouri" on the reverse side.
In his farewell address in January 1953, Truman spoke of this very specifically by asserting that, "The President, whoever he is, has to decide. He can't pass the buck to anybody. No one else can do the deciding for him. That's his job."