An inauguration is a formal ceremony to mark the beginning of a leader's term of office. An example is the ceremony in which the President of the United States officially takes the oath of office.
The most common usage of the term is in the context of a formal investiture whereby an individual assumes an office or position of authority or power. The term is usually used in reference to a politician's assumption of the duties of head of state or head of government (e.g. the President's inauguration). An "inaugural address" is the presidential speech given at this ceremony which informs the people of his intentions as a leader.
Political inaugurations often feature lavish ceremonies, in which the politician publicly takes his or her oath of office in front of a large crowd of spectators. The equivalent ceremony in another jurisdiction may be called a "swearing-in". A monarchical inauguration is similar to what in another jurisdiction may be called a coronation or enthronement.
Other than personal inaugurations, the term can also refer to the official opening or beginning of an institution or structure, for example the inauguration of a new Canada–United States border crossing.