On sixteen occasions the office of the Vice President of the United States has been left vacant due to either : 1) resignation, 2) death or 3) succession to the presidency (because the President had died in office). Prior to the passage of the 25th Amendment, the office simply remained vacant until the next election. As the wikipedia page of the 25h Amendment notes:

With President John F. Kennedy’s assassination, the need for a clear way to determine presidential succession, especially with the new reality of the Cold War and its frightening technologies,^[14] forced Congress into action.^[14] The new President, Lyndon B. Johnson, had once suffered a heart attack,^[15] and the next two people in line for the presidency were Speaker of the House John McCormack,^[16] who was 71 years old,^[14] and Senate President pro tempore Carl Hayden,^[16] who was 86 years old.

In short, the situation was ripe for one of those rare moments when the country was ready and willing to amend its constitution. A mere six years after being added to the constitution, the amendment was tested with resignation of Vice President Spiro Agnew. To take his place President Richard Nixon selected Rep. Gerald Ford to be the new VP. Under the new amendment, his appointment needed to be confirmed by a majority of both houses of Congress. It was.

And just in time. An informative post on the Constitution Daily blog explains how another aspect of the 25th Amendment, the temporary replacement of the President, was also in play as the Watergate scandal was threatening the Nixon presidency.