A holiday was a day (or date) that commemorated a religious event or occasion of a historical occurrence. In many cases, they were commemorated with a festival.

As part of his role as USS Voyager's morale officer, Neelix made a point of studying up on Vulcan holidays. He explained this to Tuvok in 2372 after declaring all Vulcan holidays to be the same. (VOY: "Meld")

Later that year, Seska chided Michael Jonas for his incompetence in performing their treasonous activities, asking him if he thought their continued communications were for the purpose of exchanging holiday greetings. (VOY: "Investigations")

Bajoran Time of Cleansing

Gratitude Festival (Peldor Festival)

Ha'mara

Christmas: December 25th

Earth Day: April 22nd

First Contact Day: April 5th

Federation Day: October 11th

Halloween: October 31st

Hindu Festival of Lights: Sunday, November 12th

Mazurka Festival

New Year's Day: Janurary 1st

Sadie Hawkins Dance: November 15th

Saint Patrick's Day: March 17th

Thanksgiving: November 23rd

Day of Honor

Kot'baval Festival

Kal Rekk

Rumarie

Tal-Shanar

Festival of T'Plana-Hath was also mentioned in the first draft script of ENT: "Fusion".

Batarael (Haliian homeworld)

Captain Picard Day (USS Enterprise-D)

Captain Picard Day (USS Enterprise-D)

Commander Riker Day (USS Enterprise-D)

Festival (Beta III)

Red hour

First meal (Meridian)

Lohlunat (Risa)

Mother's Day (Lissepia)

Prixin (Talax)

Ktarian music festival

Anniversary

Birthday

I'm Married to the Most Wonderful Woman in the Galaxy Day (according to Miles O'Brien)

Naming Day (Ferenginar)

Friday, May 8th, 2161 - Background in the Star Trek: Star Charts.

Tuesday, June 30th, 2161 - Listed on a memorial plaque at Starfleet Academy in Star Trek Online.

Wednesday, August 12th, 2161 - In the last chapter of the novel Last Full Measure, To Brave the Storm, and Control.

Sunday, October 11th, 2161 - "It's Federation Day!", a newspaper clipping created for Star Trek Generations but not seen on screen.