(6) — Bank Reserves — The Basic Picture

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Quoting from L. Randall Wray's "Modern Money Theory", page 90 ff:

[When] a government spends, there is a simultaneous credit to someone's bank deposit and to the bank's reserve deposit at the central bank; taxes are simply the reverse of that operation: a debit to a bank account and to bank reserves.

That is the whole story in a nutshell.

By spending, government pumps money into the economy and bank reserves into the accounts of banks at the central bank. Crediting the banks with reserves means that the banks are able to credit the accounts of the recipients of government spending and make the credit entries in favour of the bank's clients fungible among banks, so that all banks can settle payments for all bank clients in the banking system. [No matter with which bank one banks, payments can be made risk-free to every bank client of every bank in the banking system and payments can be received from every bank client of every bank in the banking system.]

By taxing, government withdraws money from the economy and bank reserves from the accounts of banks at the central bank. The money that had been pumped into the economy being backed up by bank reserves had been circulating in the economy, flowing from bank to bank (and ultimately to their clients) by virtue of a journey from central bank account (of a payor bank) to central bank account (of a payee bank). The journey stops when banks are asked to settle their clients' tax liabilities by debiting their clients accounts and "giving back"/debiting their bank reserve accounts at the central bank. The money is gone.

For new money to enter the system, government needs to spend it into existence.