ACH refers to a system for processing checks and/or debit cards as debit cards instead of credit cards digitally.  You can think of it as a "bank to bank transfer" via an older, traditional digital exchange system. 

The advantage to this over credit cards is typically related to "transction costs". These are typically free or may have a low cost associated.  It is or should alway be lower than the 2.5 to 4% credit card fees in the United States. 

Below are two images from Stripe's backend. If you use Stripe as a payment processer you do have the option to enable bank debit processes and or direct transfer processes in some countries.