Holidays. They don't seem too important. From Christmas to Hanukkah to Earth Day to President's Day to Halloween, most people celebrate holidays more than once a year. So why should your characters be any different?
There are three main points I'm gonna discuss. They barely scratch the surface, but I can't think of any more right this second.
First of all, holidays add to WORLD-BUILDING. It adds details to your story. Is this holiday celebrating a state/popular religion, such as Christmas? (I think plenty of atheists celebrate Christmas as well though, so be careful with that one and be specific- if your people are Christian, it'd be wise to mention it.) Perhaps it is celebrating important dead people, like President's Day? Is it celebrating nature, like Earth Day? You don't have to stick to these holidays; make one up if you want to. For example... the Gregorian Moon festival held in December celebrates the four elements in the world of Noria. Something like that. But now, Noria isn't some world you don't know or care about: you know they celebrate the 4 elements and they have a festival in December dedicated to them.
Another thing about holidays is that they can mark IMPORTANT EVENTS. An example of this is in The Scarlet Letter (by Nathaniel Hawthorne). At the end of the book, on Election Day (politics is mighty important to a town that's just starting out) Dimmesdale makes a huge, important speech, finally (sort of) confesses to his adultery with Hester, and he dies. Holidays can highlight the fact that something important is about to happen. You can start on one as well, part of that let's-drop-the-reader-into-the-middle-of-some-action kind of beginning. Or it can be somewhere in the middle, like your villain is about to set off some Independence Day fireworks as a distraction so he can slip away from you unnoticed. Or, like The Scarlet Letter, it can happen at the end, finishing your story with a grand finale.
The last thing: CHARACTER-BUILDING. Holidays can introduce facts about your character without having to come right out and saying it. For example, if your character is Muslim and you start your book during Ramadan, you don't have to outright say "Christina is Muslim." Or Hanukkah: you don't have to say "Bobby Joe is Jewish." If your character isn't religious at all, then maybe they are celebrating some holiday that they care about, like if they're an environmentalist and celebrating Earth Day. Character building is vital to a story, and adding holidays is one way of building up who they are as a person.
Holidays are an important factor to consider in your story, just as important as language or culture or history. In many ways, it actually adds to those three. Readers love a world that could they can almost reach out and touch, and knowing that Noria celebrates the Gregorian Moon festival, or that this tiny Muslim village in the Middle East during the 800s AD is celebrating Ramadan (Did they have Ramadan in that time period?) makes your story realistic and imaginable.
While this post doesn't cover everything, and I would like to elaborate more, I have to get off now (too much homework, not enough hours in a day). So, good luck with your writing, remember the points I have made, and have a blessed day. :D