Writing Excuses did a podcast on second world holidays, which I quite enjoyed. My personal favorite was Mary Robinette Kowal's advice never to "take a real world holiday and just file off the serial numbers."
I had some thoughts and they are as follows:
Some common themes in holidays, many of which overlap in single holidays:
Celebrations- something has gone well and the holiday commemorates that. Or sometimes, like Mardi Gras, it's merely a celebration of life. Birthdays, harvests, Independence days, the day Guy Fawkes didn't blow up parliament, Girls' day and Boys' day in Japan (where they celebrate basically having healthy, living children), Christmas (where Christians are celebrating the birth of a savior), wedding anniversaries, weddings themselves, the festivals for the favorite local crop (hundreds of southern US towns have peach or watermelon or strawberry festivals), and so on.
Elegies- remembering what has been lost. Memorial day, Dia de Los Muertos, more recently in the United States the 11th of September, Anzac Day in Australia and New Zealand (which is in memorium for the dead from the Gallipoli campaign in World War I).
Fertility- both human and harvest. Planting celebrations, spring dances, Valentines Day, Honen Matsuri (or Japanese national penis day (you probably shouldn't click that link at work)), Mayday, etc. Generally these tend to have a lot of plant and flower themes and decorations, even when they're not about the harvest, and chances for young men and women to show off for each other.
Memento Mori- reminder that life is fleeting and death will eventually come. This used to be a bigger thing in Western culture than it is now, but you can still see some of it in Halloween, All Saints' Day, Dia de los Muertos, and in Japan it's nominally the reason to contemplate cherry blossoms for the few days they bloom every year (hanami). Memento Mori holidays tend to be in winter.
Proving and Rites of Passage- holidays can be a time to display one's mating plumage, one's wealth or beauty, or one's readiness to be an adult. I found this article looking for the annual Vanuatu land diving festival, and it's got some good rites of passage in it, including the Ethiopian one where they line up all the village cows and have the young men run across their backs, which was the other great one I knew. A lot of festivals may have beauty pageants, strength or athletic challenges, cooking contests, riddles, puzzles, hunts, or even just lotteries (proves you're luck/blessed) with prizes and recognition for the winner.
Historical commemoration- probably the one we're most familiar with, honestly, celebrating historical people and events. Independence day, Martin Luther King Day, Cinco de Mayo, Veteran's day, Christmas (for Christians, this is a very important bit of history), any Saint's feast, President's day, Juneteenth (also known as Emancipation day), Bastille day, and so on.
Commitment to Ideals- when we pick a specific virtue we're supposed to be practicing year round and recommit ourselves to it. Lent and Ramadan (piety, temperance, and self-denial), Yom Kippur (atonement), Thanksgiving (gratitude), Mother's day and Father's day, Valentine's day. These can be some of the most important holidays in their respective cultures, and in religious cultures they often come with a hefty dose of church.
Which is a point worth bringing up. A society will celebrate its tradition generally in a way that's within the bounds of what's important to that culture. Holidays in the US almost all involve a big meal and buying things. Holidays amongst strictly catholic cultures almost always involve a special mass. Holidays in a community that's very interdependent will tend to involve at least a potluck if not an actual potlatch. Think about what's important to your society and that will help you determine if they're going to have a Ramadan or an American Valentines day.
Another major and excellent point the podcast brought up was that not everyone is going to be excited about or on board with your holiday. Plenty of people hate Christmas. It might make them feel alone, or poor, or simply stressed out by all the obligations. Fake holidays will mean different things to different people, the same as real ones do.
The best holidays I have written have tended to be made from one or more isolated pieces of real world holidays remixed and tailored to the society, with a few arbitrary decorative nods that give it the feel of specific tradition. For example, let's take something easy like gift giving from Christmas and strip away all the Christmas off it. Our holiday is primarily just the gift giving, and lots of it. Then, rather than making it a celebration for family and people you get on well with, let's toss some Yom Kippur into the mix- these are gifts of atonement and they are given to people you have wronged. For an arbitrary element, let's pick the color orange- the gifts are always wrapped in orange cloth or paper, or at least have an orange ribbon, so much so that in our society orange has this pervasive conotation of shame and wrongdoing. Picking a time of year is trickier, because it changes what the holiday means depending on where it goes: put it in fall, at harvest time, and it becomes a message of "you are in a position of excess, you should be generous and balance your accounts"; put it in winter and it not only takes on a memento mori quality, but it means people who have been wronged are getting gifts and help in the coldest, darkest part of the year, when they likely need it most; put it in spring, and the emphasis seems naturally to be new beginnings and putting old feuds behind. All of these are great, and there's a hundred potential stories that can spring up: a person who has seriously wronged someone but does not have the money to get them a sufficient gift, and must risk wronging someone else to do it; someone who holds a grudge for something serious, but receives no present or one too small to satisfy their sense of justice; someone who doesn't think they've been wronged at all, but suddenly finds themselves the recipient of a lavish anonymous gift that indicates someone did something terrible to them that they don't know about yet.
So those are my thoughts on made up holidays.