In the SCA, investiture refers to the ceremony by which a new set of landed nobility is given the leadership of their group. It most often refers to baronies, however it can also be used interchangably with the term coronation when referring to the ascension of royalty.
Example of Ceremony
Generally the first thing scheduled will be the last court of the outgoing Baronage in which the retiring Baronage will present the last of Their awards, release Their retainers and as a last point of buisness will hand over their Coronets to Their Royal Majesties.
Their Royal Majesties will then usually call the incoming Baronage into court and place the Coronets on Their heads, the new Baronage will then swear and Oath of Fealty to the Crowns and take Their place in court.
Afterwords in most cases the new Baronage will sin in state to meet their populace and recieve gifts.
Later in the day they will usually open Their first court.