Just before I was born, most money had a “Will Pay To The Bearer On Demand” line next to the value. That seemed silly: I already have $20 right here, in my hand, how am I going to get paid $20, and by who?
You see, before the Civil War, all money was gold, silver, copper, etc: precious metal, with its value set by its weight. The Civil War, however, caused significant economic trouble, and the U.S. needed to pay its public debts. So, they resolved to issue paper money, whose value was printed on its front, but not backed by any precious metals. This didn’t go over so well, because people worried that, if they got these United States Notes, people wouldn’t accept them and they would lose their value.
So, along came Gold and Silver Certificates. These were paper money specifically backed by precious metals held by the Treasury; for every certificate dollar issued, there had to be that much gold or silver in the vaults to back it.
Economies are too flexible to adhere to a physical amount of gold or silver sitting in a vault, though. Interest on loans, stock market wealth, controlled inflation, foreign currency fluctuation, and invention all bring a need for dollars without the corresponding increase in precious metals. So, the Federal Reserve appeared as a solution: they could create dollars of their own, but they had to be backed by investment in the economy. This hedged against loss of value, but disconnected money from precious metals.
So, these Federal Reserve Notes had the message “Will Pay To The Bearer On Demand” printed on them, to let people know that their Federal Reserve Notes were backed by something: the U.S. Dollar. And, if that wasn’t enough, there were still other types of money around — gold certificates, silver certificates, and U.S. Notes. So, if you were worried about your Federal Reserve Note’s value, you could go down and get your money exchanged for silver dollars, for example.
In 1933, the price of gold exceeded the value of the dollar, so the gold standard was dropped and the silver standard adopted. In 1963, however, silver was now worth more than a dollar as well, so the U.S. economy was stuck. The economic value of the dollar remained strong, but they couldn’t keep backing it by silver. So, the rules were changed: any silver certificates were to be cashed in, and all paper money afterwards would be legal tender, not redeemable for anything but other dollars.
So, starting with Series 1963 (aside from some miscellaneous silver certificates issued later to finally deplete the silver reserves), the notice “Will Pay To The Bearer On Demand” was removed from U.S. paper money, not because of some Illuminati conspiracy, but because it became the only money in the United States.