This is the most easily digestible explanation of this concept I have seen.

5.) The Fed has replaced real US currency with fraudulent Federal Reserve ‘notes,’ which are actually ‘debt instruments’—IOUs. Most people don’t realize it, but it is technically impossible to pay off a debt, because we don’t have real money with which to do so. Instead, we can only ‘discharge’ a debt. In other words, we are able to shift the burden of a debt off of ourselves by matching the amount of the bill we owe with the same amount of ‘bills’ in our wallet, owed to us by the government. We discharge the debt from ourselves to the hopelessly indebted corporate fiction masquerading as our republic, which claims US citizens (straw men corporations) as the ‘chattel’ (propery) pledged as collateral for the national debt. The whole scheme is so absurdly evil, so audaciously criminal, that most sane Americans would find it extremely difficult to believe.