Back in the days of the gold standard you used to be able to redeem a set weight of physical gold from the central bank for a dollar / pound of paper cash or minted coin. This conversion ratio was set by the central bank and acted as a final brake on inflation. When the gold standard was abolished and the dollar and pound became free floating fiat currency, it only became worth something because the government says it is. The “I promise to pay the bearer x pounds/ dollars” is just a hangover from the gold standard days when you could redeem money for gold directly from the central bank rather than through a private gold dealer. Now you can only redeem an equivalent amount of fiat currency at the central bank if day your dollar / pound note becomes damaged.
Banks can create deposits / reserves at the central bank out of nothing, they just have to promise to pay the central bank back at a later date, plus an equivalent amount of interest equal to the central bank set interest rate. This is how the central bank regulates the interest rate in the economy. If a bank charges another bank a higher level of interest for lending than the central bank, that bank can just go to the central bank instead and get charged the lower central bank interest rate. This acts as a brake on maximum inter-bank interest rates and ultimately what interest rates are charged by end consumers. The same is true for cash deposits, the central bank acts a floor / minimum interest rate for deposits as the central bank will pay interest at the central bank interest rate for deposits held at the central bank.