When it comes to implementing a checkout process on an eCommerce site, using Stripe's API can be a quick and efficient solution. By integrating Stripe into an Angular application using Netlify Functions, developers can leverage Stripe's expertise in payment processing while still maintaining control over the user experience. The project involves setting up Stripe credentials, creating a serverless function that interacts with the Stripe API, listening for button clicks to trigger the function, and making a function to load Stripe and redirect users to the checkout page. With this setup, developers can focus on building their application's UI while leaving the payment processing to Stripe.