Coinsurance is when you pay a fixed percentage of the cost of medical care after the deductible is met. For example, a health plan might pay 80% of the allowable charge, with you paying the remaining 20%. The amount paid by the insured person is called the coinsurance amount.
Not long ago, in the days before Obamacare, health insurance companies were able to control costs by using a "pre-existing condition" clause. This clause allowed them to exclude the coverage of certain medical conditions that existed before the member purchased their health insurance plan.
A pre-existing condition is classified as a medical issue that you have been treated for in the past, before obtaining new health insurance.
While this exclusion only affected individual (non-group) health plans, it made health insurance unavailable to many of the people who needed it most.