When a president gets sworn in and is in office. Inauguration is where they get the elected president in office.
Kennedy's inauguration was January 20,1961.
Technically, Ronald Reagans 2nd term ignauguration fell on the same date as Super Bowl XIX. Hpwever, since the 2oth was a sunday, Reagan has a small private ceremony at the White House. There was a second, public, ignauguration held indoors (because of freezing cold temperatures) at the Capitol January 21, 1985.