Traditions are weird, niggly things. You do them without question, but there is an unutterable logic to them. They get kidnapped and Stockholmed by other cultures (usually invading ones). They embarrass adolscents and young adults.
Above everything else, they have to have that sense of history. They have to make sense. The original Wicker Man did oodles of research, and every single song and dance and symbol has meaning (and impact on the plot). They're all traditions that Britons will be familiar with, in one form or another. The new Wicker Man reused the symbols without the research, and a lot of it, well, makes no sense. Why would earth-mother feminists dance around a giant phallus? It's meant to bring fertility to men.
Not that that stopped me dancing around one, when I was seven. But that's because the original meaning is often glossed over, and feminism takes the fore and says girls have a right to dance as well. Also, girls dancing with boys? Fertility. I was a May Queen attendant one year, which meant wearing blossom in my hair and standing behind the girl crowned Queen of the May. I don't know the history of that, but at a guess, it's a fertility thing. It usually is.
Birth and death are big in most folkloric traditions. Most Moris and Sword Dancing groups have a fool or mummer, who mugs for the crowd. Some more obviously represent death than others: the mummer with the fake horses skull? Definitely death. The German Fool covered from head to foot in black and coloured rags, with a trunk and a ponytail and a huge whip? Aside form being creepy as hell, also death; he represented the hundreth soldier, who went to the pub instead of to mass, and was the only one to the return from the battle alive (according to the programme for the 5th International Sword Spectacular, anyway).
Rebirth as a big theme as well, which is why so many celtic taditions snuck into Christian culture. That, and a lot of shoe-horning: egg rolling is a tradition around here. Good Luck and fecundity to anyone who's egg reaches the bottom of the hill unbroken. Various celtic goddess associations, but the gloss on it now is that it represents the stone being rolled away from Christ's tomb. And there's no reason it can't, as well.
Most festivals take place based on agricultural calendars. They celebrate agricultural events; the birth of livestock, the collection of harvest, and so on. They remind people when to plant crops or slaughter animals. Some take place when there's less work to do, because it's convenient, and some take place to help people cope with dark and dreary months. The events that take place are relevant to the season and to the roots of the festival (eggs at Easter, evergreen plants and a feast at Christmas). Most involve food in some way, and usually some dancing and dressing up.
Every tradition has to be justified, even if not outloud. Made up traditions even more so. Made up religions and cultures shouldn't share most of their traditions with actual ones. Characters should take things for granted. Everyone should get involved, even if it's just by turning up. There should be signficance in every unusual detail; the clothes, the food, the music, the games. There should be overlap and variation between regions and cultures. Their should be traditions subsumed by other cultures, with superficial glosses to make them palatable.
Traditions with origins 'lost in time' are annoying. If their origin is lost, then someone would have made another up, to justify continuing it. Traditions that are observed by every single person in exactly identical ways are absurd. Even festivals like Christmas vary from household to household, let alone country to country. Traditions with symbolism that doesn't match the culture need justification, and traditions that rely on objects not readily available shouldn't exist! Traditions that occur at awkward times of the year (and even on exact dates, in some cultures) are improbable. Most have some root in the agricultural calendar; you can't abandon lambing ewes to spend a week dancing around a bonfire, or disappear into a retreat during the middle of harvest.
It's easy to get sick of equinox and solstice festivals in fantasy, but at least they're dates that people would recognise and could predict (nd were less likely to be insanely busy on). That they're the same in every book is a little depressing; there's enough real world variation to give people some ideas, surely. Festivals that take place on arbitrary dates in worlds without exact calendars (which so many have, for no apparant reason) are jolting, especially if there's no tie to an event or figure. Lunar cues are great, or events like the first brith of a lamb, or the first snowfall.
Lunar calendars always make me think of months. Months are fairly standard in fantasy books as a measure of times, but I'll never understand the prevalence of weeks. They only make sense when 7 is a significant number, since there are few natural cues. But calendars, in detail, is a subject for another post.