MuleSoft is an ESB technology that can integrate on-premise and cloud applications using Stripe, an online payment provider. The Mule Stripe Connector allows developers to interact with Stripe's API to accept payments, create invoices, and manage customers and coupons. To use the connector, developers need a Stripe developer account, Stripe API keys, and to install the Mule Stripe connector. They can then build Mule flows to trigger Stripe actions like creating a customer or coupon through HTTP requests.