MuleSoft's Stripe connector allows developers to integrate their MuleSoft applications with the Stripe API to perform payment-related functions like accepting payments, creating invoices and customers. The document provides steps for setting up a Stripe developer account, configuring the Stripe API key, and using the Stripe connector in a Mule flow to create a customer and coupon in Stripe. Sample Mule flows are demonstrated to showcase how to trigger customer and coupon creation via HTTP requests.