The concept
Acquirer is the financial institution licensed by card networks like Visa and Mastercard to process card transactions on behalf of a merchant. It is the acquirer that sends the transaction to the card network, receives the approval or decline response from the card's issuing bank, and credits the approved amount to the recipient.
A payment gateway can be connected to more than one acquirer at the same time. This routing between different acquirers is what allows a second route to be tried when the first one declines a transaction, a practice known as multi-acquirer routing.
How it shows up in practice
You sell an infoproduct internationally and register an account on a payment platform. During setup, you need to choose which acquirer you want to route card transactions through. If you use more than one at the same time, the platform tries to approve the sale with the first one, and if it refuses, tries the second, increasing your approval rate without asking anything extra from the buyer.
Demonstrate to people that you can help them by actually helping them.
This automatic routing between different acquirers is what takes you out of having a single point of failure. If one acquirer starts rejecting your transactions, the other continues processing while you negotiate a solution with the first.