So, here's the story as summarized via Funimation:
The day the stars fell, two lives changed forever. High schoolers Mitsuha and Taki are complete strangers living separate lives. But one night, they suddenly switch places. Mitsuha wakes up in Taki’s body, and he in hers. This bizarre occurrence continues to happen randomly, and the two must adjust their lives around each other. Yet, somehow, it works. They build a connection and communicate by leaving notes, messages, and more importantly, an imprint.
When a dazzling comet lights up the night’s sky, it dawns on them. They want something more from this connection—a chance to meet, an opportunity to truly know each other. Tugging at the string of fate, they try to find a way to each other. But distance isn’t the only thing keeping them apart. Is their bond strong enough to face the cruel irony of time? Or is their meeting nothing more than a wish upon the stars?