Under the Affordable Care Act (also know as Obamacare), everyone (except those who qualify for Medicaid, Medicare, Veteran's benefits, or an exemption) must pay for health insurance somehow – either through their employer, the Marketplace, or their tax returns.
Yes, tax returns.
A taxpayer who does not have health insurance is required to pay the amount equal to the cheapest plan available to them at the end of the tax year. In other words, at the end of the tax year, the taxpayer will owe the total amount of health insurance premiums the taxpayer would have paid had the taxpayer been insured.
There are certain exemptions, such as the unaffordability exemption, that help the taxpayer get out of having to pay those premiums at the end of the tax year. You can find out if you qualify for any exemptions by going here.