A flat-fee you pay for treatment. Copays are a type of coinsurance, only they are a flat-fee rather than a percentage. You usually pay copayments when you check-in at a doctor's office or other medical facility (unless you're receiving free preventive care services). A copay is often a small amount (like $20 for a typical doctor's visit).
If you like the predictability of a flat-fee to see the doctor (rather than a percentage), you should look for a plan that offers copayments rather than coinsurance percentages. These plans sometimes cost more, but they lower the threshold of going to the doctor for a minor issue because you'll know exactly how much you'll have to pay.
Some plans allow you to pay a low copayment for certain types of care even if you haven't yet met your deductible. These plans often cost a bit more, but might be a good choice if you know you'll go to the doctor a few times each year.