The main way in which health insurance coverage does this comes from the way in which most Americans get their insurance. Most of us are insured through our jobs. Employers can only afford health insurance for their workers if they are relatively big companies that make good profits. If they are small or if they need to be very “bare bones” so as to cut prices as much as possible, they will be unable to afford health care for all (or any) of their employees.
The connection between this and racial minorities is the fact that many members of racial minority groups are not able to land good jobs with big companies. They might, for example, end up working at fast food places or at discount retailing outlets. Since they will not be working in highly responsible jobs, they are not as likely to be valuable enough to be given health insurance. Without health insurance, it is very difficult to get good quality medical care. The cost of buying such care out of pocket is truly prohibitive.
Therefore, our system of employer-provided health insurance hurts minorities. Minorities are more likely to work in jobs that do not provide health insurance. This ends up causing them to have much poorer access to health care.