Harry Potter series is a prime example. Hogwarts School of Witchcraft and Wizardry is bursting with traditions including Houses, Tournaments, a Sorting Hat, and Deathday parties. But there are also traditions that help round out the wizarding society at large. For example, on Harry's seventeenth birthday, The Weasley's gave Harry with a watch. Not only was it a traditional gift for a wizard who has just come of age, but it was also a family heirloom. This signified that the Weasley's considered him fully grown, and most importantly to Harry, a part of the family.
Traditions are also important because they form community. Whether it's the celebration of a holiday, the ritual of a Japanese Tea Ceremony, or singing Take Me Out To the Ballgame during the seventh inning stretch, it brings people together in a common activity or belief. There are three ways this can help your story.
1) People love to belong to things. We need a sense of community to thrive so it's natural so seek out like-minded people. Those kids who go out for pizza on Fridays, people who drive Jeeps, and even writers (like me) who participate in NaNoWriMo every year, they all have a sense of belonging to something. It often strengthens their self-identity and helps influence the decisions they will make. Will they go along with what their peers want them to do? Or not?
3) Rules (traditions) are meant to be broken! Not everyone fits into the roles they are expected to play. Katniss Everdeen and Peeta Mellark, Bilbo Baggins, Tris Prior, Scarlett O'Hara, and Maximus Decimus Meridius (a.k.a. Gladiator), are all good examples of characters who did the unexpected and challenged the rules of their society. In the Hunger Games, Peeta bucked the tradition of the games by refusing to think of Katniss as an enemy. He lied, manipulated the audience, and fought to ensure her survival - even if it meant the cost of his own.
As you write, consider the traditions your character might have. Do they give your character a sense of family or community? Are there traditions in the character's society that help develop the setting? How do traditions help or hinder your characters as they struggle through their journey? Your story will be richer for the traditions you choose to bring into your character's life.