Hyperion starts as a story about seven people going on an impossible journey. Then, Sol Weintraub has to go and ask, "'Does anyone here know why he or she was chosen by the Shrike Church and the All Thing to go on this voyage?'" (1.77). Way to go, Sol. That changes the whole structure of the novel, turning it into a story about stories. And they often share these stories after a meal, letting the roast beef and sky squid settle in their bellies, having a nice drink, and spinning some amazing yarns.
Sounds like Friday night chez Shmoop.
But really, listen to what Sol says:
I suggest that we share our stores in the few days remaining to us. [...] It would—at the very least—amuse us and give at least a glimpse of our fellow travelers' souls before the Shrike or some other calamity distracts us. Beyond that, it might just give us enough insight to save all of our lives if we are intelligent enough to find the common thread of experience which binds all our fates to the whim of the Shrike. (1.90)
Let's break that down: first, Stories help pass the time. Second, they help people get to know each other. But more than that (third, if you're keeping track), is that stories save lives. Whether they realize it or not, the pilgrims are telling stories that get to the heart of the universe and human experience. They tell stories about love, children, death, religion, and intergalactic space travel.
And what that means is that everything, and everyone, is a part of a story. And what that means is that we're all connected through the power of storytelling. "We represent islands of time as well as separate oceans of perspective" (1.100), says Weintraub. Stories build bridges between these islands.