What does EFT master - ACH mean on your bank statement?

Answer 1

Electronic Funds Transfer - Automated Clearing House.

Fundamentally, this is an "electronic check", there is a Federal Reserve system whereby a company is provided with your checking account details (routing number and account number), and then they can debit your account just as if you wrote them a check, but without the overhead of handling the paper check.

You have to authorize this to be done, but that authorization can be as simple as writing a check at a store where the cash registers display a notice "By writing a check, you authorize us to convert it to an e-check" (or similar language). It is becoming increasingly common, particularly at large retailers that handle lots of checks. It is also very common online.

This is less expensive and faster for the banking system, and can be less expensive for the company handling the check. There is no practical difference to the consumer than if you had written a paper check, other than that there is no check to be stored.

For legal purposes, the record of the ACH transaction has all the legal weight of a paid check for purposes of showing a bill was paid, etc.