Person-years are used to calculate incidence rates of cancer. This is commonly done in cancer studies because cancer takes years to develop.
For example, suppose we have 10,000 people and they’re all followed for 10 years after some treatment, that’s a total of 10,000 x 10 = 100,000 person-years. If 50 people die within these 10 years, then the mortality rate would be 50 per 100,000 person-years.