What event led to John Tyler becoming president of the U.S.? Why was it significant?

Answer 1

William Henry Harrison was elected President in 1840, with Tyler as his running mate.
Harrison, who was 68 years old, caught a cold during his long inaugural address, and died of pneumonia on April 4, 1841, after only a month in office.
This was the first time that the Presidency had become vacant, and the Constitution is ambiguous about the Vice-President's succession. Article II, Section 1 reads: "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 upon the Vice President..."
What is the antecedent of "the same"? Does it mean "the said office" or "the powers and duties of the said office"? In other words, does the Vice President become President, or does he become Acting President?
Most Constitutional scholars would say that the writers of the Constitution intended the Vice President to become Acting President, but Tyler took command of the situation and declared that he was indeed the new President, and thus it has gone ever since when the office of President has become vacant.
In the long run, this strengthened the office of President, which had been intended to be Constitutionally rather weak. Incrementally, the office of President has become much more pwerful over the intervening 166 years, and the current president has arrogated tremendous power to the office in the last six years.

Answer 2

greyguy's got the answer. Just a little Constitutional addendum to the matter --

Tyler's action (imitated by others in the same situation) was finally, formally made part of the Constitution with the ratification in 1967 of the 25th amendment.

The first section reads as follows:
"In case of the removal of the President from office or of his death or resignation, the Vice President shall become President."

(Historical irony -- the succeeding provisions in this amendment were invoked under the VERY NEXT President elected. VP Spiro Agnew resigned, and was replaced by Gerald Ford under the terms set out in this amendment. He later became President with Nixon's RESIGNATION [first by a President], and Nelson Rockefeller became VP by the same method as Ford)