The "change of responsibility" ceremony is a military tradition. The Army holds the ceremony when a senior non-commissioned officer leaves a leadership position and a new NCO takes his place. Army Toolbag.com says that it serves two purposes: It renders honors to the departing NCO and provides official recognition of the new leader.
NCOs
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Non-commissioned officers are enlisted personnel in positions of leadership, unlike captains or colonels, who receive their positions as "commissions" from the government. The highest-ranking NCO is the sergeant major of the army. Below her come the command sergeant major, sergeant major, first sergeant, master sergeant, platoon sergeant, sergeant first class, staff sergeant, sergeant and corporal.
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The NCO Sword
The symbol of an NCO position of responsibility is the NCO sword. The Army says that when an NCO is transferred and a new officer replaces him, the symbol of the change and the heart of the ceremony is when the sword is passed. As the transfer orders are read, the departing NCO hands the sword to his replacement, which will hand it back to the appointed sword bearer.
Meanings
The "Belvoir Eagle" newspaper says the sword is no longer part of the NCO's equipment as it would have been 200 years ago, but using it in the ceremony reminds the soldiers that the senior NCO is responsible for order and discipline. It also reminds the NCO of his responsibility to care for the troops.
The Opening of the Ceremony
Army Toolbag.com describes one 2007 change of responsibility ceremony for a command sergeant major in an Army joint task force. First, the units in the task force enter in formation and take their seats. Then music plays as the official party, including the past and future NCOs, enters. If a general is in the party, the music adds one "ruffle" for each star he has. Then come the national anthem and the invocation.
The Passing of the Sword
The narrator of the ceremony will read the histories and accomplishments of both men, who will then step into position for the change of responsibility. The NCOs then carry out the sword ritual. Each NCO will then make a speech, after which the ceremony concludes.