Federation Day is a day of celebration commemmorating the founding of the Federation in the year 2161.
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 Enterprise in 2368. (TNG: "The Outcast")