Learn more about President-elect
A President-elect is a political candidate who has been elected president but who has not yet taken office, as it is still occupied by the outgoing president. Similar terms can be used depending on the type and level of government, including prime ministers-elect, mayors-elect, governors-elect, etc.
 United States
In the United States, the members of the U.S. Electoral College are elected in November once every four years, and the Electoral College in turn elects the President of the United States in December, and finally the President-elect assumes office in January. One is officially the president-elect only after being chosen by the Electoral College, but unofficially the person chosen in the November election is called the President-elect even before the Electoral College meets. An example of the practical effect of the official status is found in the U.S. Constitution's provision that if the President-elect dies, then the Vice President-elect becomes president on Inauguration Day. That rule takes effect only after the meeting of the Electoral College. If the person unofficially called the President-elect dies before that meeting, then the Electoral College would have broad discretion to choose some other person.
US Presidential elections are held in November, but the President's term of office does not expire until January 20 of the following year. Presidents, or and other politicians, will usually assemble a "transition team" of some sort, to prepare for a smooth transfer of power following the inauguration. The President often works closely with the President-elect on important policy matters during the last three months of the President's Term, so as to ensure a smooth transition and continuity of operations that have significant national interests.
During this time, the President is referred to as a lame duck because he has already accomplished about as much as he possibly can to promote the policies and agendas of his administration, and is usually not in a position to make very substantive decisions.
At exactly 12:00 noon, on January 20 following an election year, the Term of Office of the President expires by Constitutional mandate, and the President-elect becomes the President of the United States. This has been the source of many misinterpretations, and urban legends, such as the David Rice Atchison presidency theory, which is not only predicated upon false assumptions, but is also logically flawed. Office holders-elect do not exercise the powers of their office until they take the oath. The Oath is an executing legal instrument and does not affect the automatic accession to and occupation of the Office of the Presidency, which, in the case of the US President, proceeds, ipso facto, from the expiration of the predecessor's term.
 Non-elected officials
When politicians are not elected, they are usually called the "designate" until formally assuming office. For example, the "Secretary-designate" or the "Vice President-designate." This title is occasionally used for Prime Ministers as well, to reflect the fact that they are not usually directly elected, but instead formally appointed by the head of state according to the rules of the parliamentary system.