It doesn't, really.
But here's the logic:
1) Congress has the power to "coin money."
2) Congress has authorized the Treasury to make platinum coins, in whatever denomination. The intent was to make novelties for coin collectors, but the coins will still be legal tender - at face (not metal) value.[1]
1 + 2 = 3) It's legal for the Treasury to make a one-ounce platinum coin and stamp it "One trillion dollars." Or, $1,600 in metal and $999.999,998.400 in seigneurage.[2]
4) The Treasury then deposits that coin at the Federal Reserve and writes checks or other disbursements against the trillion dollars that they suddenly have in their account.
Take away the smoke and mirrors, and it's the coin version of running the printing press.
[1] We already see this with pennies. They're "worth" a cent in face value, but actually have something like 1.4 cents' worth of zinc, each. They would literally be worth more, hammered flat and sold as scrap.
[2] Literally, means the right of a sovereign to profit from making coins. In context, it's a polite word for "inflation."