The Festival was a short period of anarchy and debauchery on the planet Beta III which began at the red hour.
During the Festival, normally placid citizens of Beta III exploded into paroxysms of lust and destruction. Twelve planetary hours later, the Festival ended, and the people resumed their calm and tranquil state, oblivious to the chaos they had created. Some of this calmness may have been a front, since at least one case was observed of a woman raped during Festival breaking down and crying once indoors afterwards.
At a certain age, a citizen of Beta III was to be considered "excused" from the Festival. The one case in which this was observed pertained to a group of elderly men who stayed indoors during one such Festival. All other able-bodied persons were expected to immediately participate in the Festival the minute that the red hour struck. To engage in any other activity, even delaying for a few minutes to tend to business pending after the festival, was considered totally unacceptable.
The manner in which the Festival was conducted may have varied in different areas of Beta III. One such comment was made about the Valley, which was said to have "different ways" and thus it was considered marginally acceptable that a landing party from the USS Enterprise (posing as people from the Valley) did not outright participate in the Festival. Even so, to not participate in the Festival at all, known as "scorning festival", was considered a very serious crime and could be reported to the lawgivers. (TOS: "The Return of the Archons")