What it does is require you to show proof of coverage to get your state income tax returned to you...
Okay... not totally clear. "your income tax returned to you? I can only assume you don't get your entire income tax returned to if you have coverage. Can you be more precise?
Does it mean that a portion of your tax is some kind of a health care levy which is returnable only if you can show proof of health care coverage?
Buying it is legally required, to make sure there are enough healthy people paying in to meet the costs of the people with pre-existing conditions.
It means, if you don't have a documented health plan, and you paid in too much income tax to the state, then your refund of overpaid tax, all or in part, can be kept by the state. Ostensibly to help pay off the cost of whatever care you used during the year but did not pay for in the form of private insurance and thus took from the state. The Federal level ACA (Obamacare) was similarly modeled and this was called the "individual mandate" and worked similarly: if you didn't have proof of coverage, it made the most sense to avoid overpaying taxes (because you wouldn't get a refund).
Okay, I think that now I understand better why Americans are not so enamoured with the ACA - it's pretty hard to see how this system isn't overly complicated & opaque, doesn't spuriously involve the state, and how it acts in a way that is fair (both fairness wrt to burden-sharing and the specifics of penalizing undesired behaviour).
I'd caution against conflating the term 'individual mandate' with this weird tax-deduction penalty whaggamathingy - Not merely to accommodate my OCD, but also because it's easy to imagine that when people debate healthcare systems and compare the ACA to other designs that feature a legal requirement to have insurance (like the Austrian, Belgian and German ones), they will be tempted to assume that the latter also feature this weird income tax-return penalty thingy. That is
not the case (not entirely certain about the Austrian & Belgian systems, but it would surprise me if they did).
Your insurer is legally required to double your premiums for every month you are uninsured after the first month, period. No involvement of the state executive or its IRS-equivalent.
This is less pro-oligarchy than it sounds, as 87% of Germans are insured with "Krankenkassen" (lit. "Sickness-funds"), who are not strictly speaking companies with a profit-motive, so its pretty obvious you are burdening your peers by not being ensured, rather than "sticking it to the man". Krankenkassen are more like a kind of mutual funds whose sole purpose is to invest in the healthcare of its members. Germans would distinguish between "Krankenkassen" and "Krankenversicherungen" (Sickness-insurances) - both are insurers, both are privately run, but only the latter are bona-fide companies with a profit motive.
On the flipside, nobody can be refused basic-plan insurance, for any reason at all, period. The Krankenkassen cannot refuse anybody, no matter what plan people want to enroll in; the private insurance companies can refuse to take someone into one of their higher-tier plans. But basic care is covered for every homo sapiens in Germany (yes, also non-citizen residents).
Same simplicity with the premiums: Your premiums are fixed at 14.something% of your non-deductible income (where 'non-deductible' probably means something different than it means in the US, so take with grains of salt). Your employer is required to pay half of that, so in the end, everybody pays about 7.something% of their income for healthcare, nobody can be denied basic-plan coverage, and the decision about what treatments are considered basic plan is made periodically by public panels staffed with representatives from stakeholders (care workers, insurers and patients), that are overseen by the government (in an Ombudsman-role). Pretty similar to how unions and employers handle working-rights disputes.
The details are complex and not widely known even to natives, but the principles are fairly simple. Goes back to Bismark's horror of burdening the state with social care costs - the state is just involved enough to make sure that the system works, but otherwise it was designed for autonomous function.
Anyhow - thanks to everybody who helped educating the furriners.