So: by popular demand (my mum) a quick guide.
The 25th amendment was ratified- i.e. became part of the US constitution in 1967. The amendment is basically about clarifying the presidential and vice presidential succession.
You see, Article 2 of the Constitution says "In Case of the Removal of the President from Office, or of his Death, Resignation, or Inability to discharge the Powers and Duties of the said Office, the Same shall devolve on the Vice President"
But this is quite vague.
So when W.H. Harrison was the first president to die in office in 1841, it wasn't really clear what powers his VP, John Tyler, would have, nor what he would be called (president? acting president?)
Tyler took the oath and became president. This set a precedent.
Until the 1960s, convention dictated that if a president died in office, then their VP became president, was called the president, and had the powers of the president. Fine.
But this was not spelled out in law. And there were some outstanding questions:
1. If a VP becomes President, then how is the VP replaced?
2. What if the president is unwell, or unable to perform his role for some other reason? How can that be managed?