Advanced Premium Tax Credit
  
The Advance Premium Tax Credit is a government subsidy for health insurance that was part of Obamacare, aka the Affordable Care Act, and was put in place in 2010. Under this provision, the government pays part of a person's health insurance bill by sending a check directly to the insurance company. It's called a "tax credit" (i.e. you get a rebate or a deduction, so you pay less tax), but in practice, it's a direct payment from the federal government to the insurance company.
The "advance" part comes in because the government is letting you take the tax credit right away, rather than forcing you to wait for all the tax filing rigmarole. Basically, the government loans you the money you expect to be credited based on your income, but the loan only works for buying health insurance. The catch is that, if you estimate your income wrong and end up getting less of a credit than you predicted, then you'll have to pay the difference when your taxes come around.
Why does the government take such pains to do this edge paperwork? Because too many people go bankrupt waiting for health insurance to pay them the dough owed. So rather than lean on the insurers, i.e. making it illegal for them to be opaque in what they charge and how they reimburse, the government just uses taxpayer dollars as a buffer. Fair? Not fair?