Despite Mr. Trump’s tweet that he has a “much bigger & more powerful” button than Mr. Kim, the fact is, there is no button.

There is, however, a football. Except the football is actually a briefcase.

The 45-pound briefcase, known as the nuclear football, accompanies the president wherever he goes. It is carried at all times by one of five military aides, representing each branch of the United States armed forces.

Inside the case is an instructional guide to carrying out a strike, including a list of locations that can be targeted by the more than 1,000 nuclear weapons that make up the American arsenal. The case also includes a radio transceiver and code authenticators.

To authorize the attack, the president must first verify his identity by providing a code he is supposed to carry on him at all times. The code, often described as a card, is nicknamed “the biscuit.”

In his 2010 autobiography, Gen. Henry H. Shelton, chairman of the Joint Chiefs of Staff during the final years of Bill Clinton’s presidency, wrote that Mr. Clinton had lost the biscuit for several months without informing anyone.

“That’s a big deal,” General Shelton wrote, “a gargantuan deal.”

The president does not need approval from anyone else, including Congress or the military, to authorize a strike — a decision that might have to be made at a moment’s notice.