PlanetScale is a serverless MySQL-compatible database that aims to solve scalability challenges faced by backend web servers. It offers features such as intuitive developer workflows, advanced query monitoring, and the ability to instantly revert schema changes. By replacing traditional database upgrades with PlanetScale, developers can focus on optimizing their application's performance without worrying about provisioning new instances or increasing database capacity. The tutorial demonstrates how to set up a Django application to use PlanetScale, including connecting to the development branch, running migrations, adding data, and promoting to production.