The MongoDB Stitch platform allows developers to create triggers that react to changes in their data using change streams, enabling real-time data processing and integration with downstream systems. To solve the Trigger Challenge, developers must create a Stitch application linked to their cluster, define a trigger that captures specific events, and write a Stitch function to process those events. The solution involves creating a trigger that counts documents meeting certain criteria in a sales collection, using MongoDB change streams to capture real-time inserts and update operations. The function increments a running total stored in the database, demonstrating a simple example of real-time data processing and integration with downstream systems.