It means orders that are clear, specific, and that are to be followed right now.
"My wife gave me my marching orders--I'm to go to the supermarket right now and bring back a gallon of milk and two loaves of bread."
In Clinton's case, it means that she could not begin immediately to implement the various elements of her program, because she and everyone else would know that the people who voted for her were only voting against Trump, not necessarily because they supported her proposals. She gets her "marching orders" from the will of the people, and the will of the people would not be clear.
"Marching orders" is obviously a military expression but I don't know what the literal military meaning is.