What does the twelfth amendment prevent?

It prevents someone who is constitutionally ineligible form being Vice-president or president. 

The Twelfth Amendment to the United States Constitution provides the procedure for electing the President and Vice President.Problems with the original procedure arose in the elections of 1796 and 1800. The Twelfth Amendment refined the process whereby a President and a Vice President are elected by the Electoral College. The amendment was proposed by the Congress on December 9, 1803, and was ratified by the requisite three-fourths of state legislatures on June 15, 1804. It makes sure one is constitutionally eligible to be president/vice. So it prevents un-eligible people from being in office.