The Constitution (Article II, Section 1) provides that "Congress shall determine the Time of choosing the Electors, and the Day on which they shall give their votes; which Day shall be the same throughout the United States." In 1792, Congress established legislation making the first Wednesday in December as the day on which presidential electors were to assemble and vote, and further required that the States appoint electors within 34 days prior to the date set for the electors to vote. In 1845, Congress established legislation providing a uniform date for the choice of electors in all states, establishing "Tuesday next after the first Monday in the month of November of the year in which they are to be appointed." The last Presidential election was held on November 6, 2012. The nation went to the polls and re-elected the 44th President of the United States, Barack Obama.
The decision to create a single day for the selection of Presidential electors was intended, in part, to prevent election abuses. The reason that November was chosen was that the United States was largely a rural and agrarian nation. Since the harvesting of crops was normally completed by this time, farmers were free to vote. Also, since November is before the onset of winter, traveling would be easier (particularly in the northern states that experienced harsh winter weather).
Why Tuesday after the first Monday?
Tuesday was chosen partly because it gave a full day's travel time between Sunday, which was widely observed by religious groups as a strict day of rest (except for traveling) and voting day. Two days were given for travel to give voters the time to travel by foot or by horse to the nearest polling place, usually the county's political center (seat).
Finally, the choice of Tuesday after the first Monday was established to prevent elections from falling on the first day of the month. The first date of the month was typically reserved for court business at the county seat and would not make a good day to hold elections. By making the Tuesday following the first Monday in November election day, Congress had insured that this would not happen.