This counts every accept response this server has sent, including ones the client might later reject as invalid, for example due to a bad signature from a shared-secret mismatch. A discrepancy between this counter and actual successful logins reported elsewhere would point the admin toward checking for a shared-secret problem specifically on this server's row. For example, this counter climbing steadily while users still report being denied access would suggest the accepts are arriving but failing validation, pointing at the shared secret configured for this server.