A property of an operation: calling it twice with the same input produces the same result as calling it once. "Charge customer $50 for invoice #12345" should be idempotent—if the network drops and you retry, you don't want to charge twice. Idempotency is one of the things separating "this works in a demo" from "this is safe to run at scale."
Their payment endpoint was idempotent, so retrying a failed charge couldn't accidentally bill the customer twice.