The electoral college system of America requires a candidate to obtain an absolute majority in order to become elected to the presidency. To have an absolute majority means that the candidate has over half of the total possible votes, which is different from a simple plurality, which only would require that candidate to have the most votes out of all the candidates.
This necessity for an absolute majority means that, while such occurrences are rare, it is possible for no candidate to win the election, as no candidate could successfully achieve the absolute majority necessary. Such situations were anticipated by the Constitution’s framers, however, and some provisions and procedures were laid out to determine how such a problem should be solved.
The electoral college system was designed so that a candidate would have to achieve an absolute majority in order to prevent one candidate becoming the President of the entire nation, simply because he received all the votes from his home area, which were enough to put him over the other candidates. Requiring an absolute majority ensures that over half of the nation would have voted for that candidate, although of course the exact proportion would vary depending on a number of different statistics.
But because the American system is also not a definitively two party system, and does allow for any number of possible parties to run, then the available electoral votes might be split between enough parties so as to prevent any one candidate from achieving that absolute majority. This was most likely one of the primary worries of the framers of the Constitution with regard to the electoral college system, as there were no parties or clear political organizations at the time they were writing the Constitution, and they could not have been certain that hundreds of different candidates would try to run, and would each eat up just enough votes to prevent any one candidate from successfully winning the presidency.
As such, they included a contingency in Article 2 of the Constitution which would dictate proper procedure in such situations. Specifically, the House of Representatives would perform a vote to determine the President. This system was further refined after the election of 1800 with the Twelfth Amendment. To find out more about the base system for solving the problem of no absolute majority, follow the link.