Federation Day was a day of celebration commemorating the founding of the United Federation of Planets.

A card game called "Federation Day" poker existed in the 24th century, in which "2"s, "aces", and "6"s were wild, since the Federation was founded in 2161.

Deanna Troi suggested playing this game to the rest of the senior staff members of the USS Enterprise-D in 2368, however, Worf found it difficult to ascertain exactly what he had in his hand with so many wild cards. (TNG: "The Outcast")

In 2161, after the charter was signed, ratifying the Coalition of Planets, which ultimately lead to the formation of the United Federation of Planets. (ENT: "These Are the Voyages...")

Counselor Deanna Troi's line in " These Are the Voyages... ", in which she states "this alliance will give birth to the " suggests that the charter which Archer was to sign at that point in 2161 was not the Federation Charter, but rather the charter of the Coalition that led to the Federation's incorporation. Since the Federation has already been confirmed to have been incorporated in 2161, this would seem to indicate that the Coalition gave way to the UFP within the same year. It is also possible that the Coalition of Planets was simply renamed the United Federation of Planets later in the year, in which case, the charter which Archer is about to sign in this episode may be considered the Federation Charter. this alliance will give birth to the Federation

Background information

Non-canon sources have established several dates for the event: