As one non-racial example there was a pneumonia detection model that got some pretty (at least amongst people interested in radiology and deep learning) where the model was detecting the metal badge the hospital was using when taking scans (so every xray from this hospital had a similar graphic on it). This hospital had a higher pneumonia rate as it generally had older people going to it, and because of this the model started giving everyone who went to that hospital a higher likelihood of having pneumonia. So essentially it picked up on the age based bias of the hospital itself.
This is an issue in other types of medical data as well. There have been multiple studies that show doctors are less likely to successfully diagnose a heart attack in women than in men, and that doctors will also underestimate how much pain a black man is in compared to any other category. Those biases end up in the data itself, so if you naively train your models against that data they too will make similar mistakes.