A Thematically Significant Patient
The patients come in with injuries, medical anomalies, surgeries, illnesses, or whatever other kinds of miscellaneous trauma they can throw the doctors' way. The medical problem, though, is always pretty innocuous. More often than not, it's the backstory or emotional arc of a patient that will always closely mirror one of the doctors.
It's happened all the way up to season 13. Here's an example: in the second episode of the season, Jo has been assigned to a patient with a brain tumor. At this point in time, Jo is in the midst of a tragic breakup with Alex. The patient tells the story of her horrible 30-year marriage to a preacher who cheated on her. She explains why she stayed in the marriage for so long. She talks about how she made herself small. Her tumor changed everything, she says. "I had to start looking out for myself. I walked right out that door with a tumor the size of cantaloupe in my head. Stronger because I had to be." Jo suggests the tumor made her brave, but she says, "No, she made me pissed. Being pissed made me brave."
The exchange is just the "a-ha" moment Jo needs to realize she can walk away from Alex. She can be pissed, and she can be brave, and she can be strong. These sorts of epiphanies, handed down from patients, are basically a cornerstone of the show. It's how the doctors gain clarity, time and time again.