This amendment is a bit long, so I’m going to put a read-more cut before it. This amendment affects the Electoral college, so if you are interested in that, considering upcoming events, this is a good one to look into.
It was passed by Congress in December 1803, and ratified in June of 1804. It relates to Article 1, Section II on the elections of Presidents and Vice Presidents as well as Amendments 20 & 22 , which actually edits part of this amendment.
The Electors shall meet in their respective states and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President, and they shall make distinct lists of all persons voted for as President, and of all persons voted for as Vice-President, and of the number of votes for each, which lists they shall sign and certify, and transmit sealed to the seat of the government of the United States, directed to the President of the Senate; — The President of the Senate shall, in the presence of the Senate and House of Representatives, open all the certificates and the votes shall then be counted; — The person having the greatest number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in case of the death or other constitutional disability of the President. — The person having the greatest number of votes as Vice-President, shall be the Vice-President, if such number be a majority of the whole number of Electors appointed, and if no person have a majority, then from the two highest numbers on the list, the Senate shall choose the Vice-President; a quorum for the purpose shall consist of two-thirds of the whole number of Senators, and a majority of the whole number shall be necessary to a choice. But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States. (Source)
The original electoral college worked by each delegate voting for two people, at least one of which had to be from a state not the delegate’s. Whatever candidate got the most votes got to be president. The second place winner would become Vice president. Only after the 1796 and 1800 this turned problematic as parties started to form around key governmental ideals. There was the Federalists (As you may have guessed, they were for a strong government) and the Democratic-Republicans (who were for a smaller federal and stronger state governments). John Adams was a Federalist, while the Vice President who got elected was Thomas Jefferson, who was a strong Dem-Republican.
Basically, if we translated this into modern politics, and we went by the current standings that would mean Donald Trump was President and Ted Cruz was Vice president. Or (for those of you who were Democrats) Hillary Clinton was President and Bernie Sanders was Vice President. Of course those are along partyish lines (Sanders is registered independent). In the actual elections it wasn’t like that. John Adams won the most votes, but his party was split on the second vote, which allowed Thomas Jefferson to become vice president. These two men didn’t get along professionally. Personally, they were undecided.
So in 1797 a Senator suggested they changed the way the electoral college worked. His motion didn’t gain much attention but after the 1800 election, it was decided something needed to be done and the 12th amendment was formed.
After this point, Vice presidents were elected by separate ballot. It still wasn’t quite the way we have it now, but delegates would vote for the President on one ballot, and the vice president on another ballot. The hope was this would make the President and Vice President more likely to get along, and run things a bit more smoothly.
Not that there isn’t problems with this amendment. The 20th (which amends timelines), and 22nd Amendments (which amends term limits) are also about presidential elections. This also amends what happens when the electoral college fails to elect a president and a vice president. This has happened once for each position but not in recent history (the last being 1836).
This amendment came up during the 2000 contested election of George W. Bush, when several voters claimed the election to be false due to Dick Cheney and GW Bush being from the same state (Texas).
Oddly enough, 2 states failed to ratify this amendment. Delaware and Connecticut did not ratify this amendment. New Hampshire was disputed as the legislature ratified it but it got vetoed by the Governor. However 13 other states ratified it, allowing it to be ratified in 1804. Massachusetts originally rejected the amendment but ratified it in 1961, though I’m not sure why they felt the need to do it at that point. Then again, there are some states that didn’t even weigh in. I suppose if you come into the union after a ratification it doesn’t really need your input.