For example, payroll payments are usually handled this way. The tape is sent to an ACH, and together with information from other banks is read into a computer. Payment instructions are passed on, and payments to and from the various banks are netted. Settlement of net positions is made over Fedwire. ACHs handle both credit transfers and debit transfers.
Credit transfers are similar in nature to giro payments, e.g. direct deposits.
Debit transfers are similar in nature to checks, e.g. authorizing your insurance agency to take monthly payments from your bank deposit. In the U.S. most ACHs are operated by the Fed, although there are private operations too. .