According to Cornell University Law School, the 25th Amendment is considered important because it established succession in case the President of the United States dies, resigns, is impeached or is otherwise unable to fulfill his duties. Prior to the 25th Amendment, there were only vague rules that explained what to do if the office needed filling in the middle of a president's term.
According to Wikipedia, the 25th Amendment was ratified in 1965 due to the efforts of Senator Birch Bayh of Indiana and Representative Emanuel Celler of New York. In the wake of John F. Kennedy's assassination two years before, the U.S. government realized that there was no clear line of succession to fill a vacant presidency. To combat this, Senators Bayh and Celler proposed a bill to enable the vice president to fill the vacancy. This amendment also clarifies what to do if the vice presidency needs filling, as well.
According to the Gerald R. Ford Presidential Library and Museum, the 25th Amendment was first used in 1973, when President Richard Nixon nominated Representative Ford to take up the vacancy left by Vice President Spiro Agnew when Agnew resigned. Less than a year later, Nixon resigned, Ford became president. As a result, Ford nominated Nelson Rockefeller to be vice president.