The MongoDB World Weekly Challenges, specifically the fourth week's challenge, required building a basic API using Stitch's Rules and Webhooks features to provide three incoming webhooks: search-listings, add-swagpref, and get-swagprefs. The solution involved creating a user for the webhook to run as, configuring data visibility via Stitch admin UI rules and filters, applying query filters to limit relevant results, setting up an HTTP service interface for the webhooks, implementing the webhook functions using JavaScript, and validating schema for employee swag preferences collection. The test suite included various tests to verify the correctness of the API implementation, with most tests initially failing due to incomplete configuration but expected to pass once implemented correctly.