It is a ceremony to mark the beginning of a new four-year term of the President of the United States.
The ceremony takes place for each new presidential term, even if the president is going to continue in office for a second term. Since 1937, the inauguration has taken place on January 20, which is 72 to 78 days after the November presidential election-which is on the first Tuesday after the first Monday in November.
The term of a president begins at 12 noon on the day of the inauguration, when the Chief Justice of the United States has the new president recite the oath of office. However, if January 20th falls on a Sunday, the Chief Justice of the United States has the new president recite the oath in a private ceremony behind closed doors. Then, on the next day, Monday January 21, the new president recites the oath publicly at the inauguration ceremony.
The repeating of the presidential oath of office in public is the only component of an inauguration ceremony mandated by the United States Constitution in Article II, Section One, Clause 8 (read it for yourself here).
However, over the years, various traditions have been added to the inauguration ceremony. The inauguration went from a simple public oath-taking to a day-long event, including parades and many social gatherings.