The MongoDB Stitch Serverless Platform has announced a new feature called Stitch Hosting, which allows developers to host, manage, and serve static media and document files. The author of the blog post took their PicStream React app and hosted it in a Stitch app, enabling it to be served as static content from the mongodbstitch.com domain. To achieve this, the author used Webpack and Babel to create a single static bundle.js file, which was then configured to serve the application's static files through the Stitch Hosting feature. The author successfully uploaded their static files to the hosting platform and accessed their website using the provided DNS name.