Think of writing a braided story just as you would make a braid in someone's hair: despite separating the hair into three distinct sections, each section ends up overlapping with each other until you create the braid. A braided story works in a similar fashion. Each experience/story could stand on its own, but when placed next to one another, shared themes, motifs, and symbols are illuminated—giving not only greater depth to the other sections but also greater weight to the overall story arc.
Take F. Scott Fitzgerald's The Great Gatsby, for instance. Although not an exact example of a braided story, the work does employ some braided story techniques that may be helpful as you craft your own braided story. As you read The Great Gatsby, you notice that Nick Carraway, the first-person narrator of the novel, tells a lot of stories that, at first, may not seem on-topic or relevant to the topic at hand. Nick starts off by talking about his own personal history and brief introduction to Gatsby in chapter 1, only to switch gears in chapter 2 to the history of the "valley of ashes," the urban expanse of land that connects the Eggs of Long Island to the borough of Manhattan and contains those ever-watching billboard eyes of Doctor T. J. Eckleburg. Although the connections of these two stories may not make logical sense at first, by book's end we come to realize the significance of the valley of ashes when it comes to the shifting identities of characters and the plot as a whole.
What would you like to communicate to your readers? What would you like them to learn from your experiences and stories? As you braid your own stories, look to see if there are any symbols, metaphors, or themes in one experience that can mirror or better explain the symbols, metaphors, or themes of the other. If you find that you cannot find any connections, keep digging. What you're really trying to write may be just below the surface. You've got this!