What is an ACH remittance?

This can have two meanings:
ACH by de facto is a US concern, ACH stands for Automated Clearing House, which is in some manner a very antiquated system for clearing of cheques electronically.

If a payment is being made to you via an ACH submitted cheque or if you are paying someone via ACH submitted cheque, this can be termed as an ACH remittance (in most circles this is called an ACH payment simply).

However, if you are sending money cross-border (remittance) and are paying via an ACH cheque, this would correctly be termed as an ACH remittance.

ACH remittances are usually done online on websites like Xoom.com, Remit2India.com, etc. where the financial instrument of choice to make the payment is your bank account, and you utilize the ACH system to present an e-check or electronic cheque (sometimes also called an Internet check) to make the payment for your remittance.