It can be hard to learn a new tool without having something you want to accomplish. These tutorials will at least guide you through particular use cases to show you how you'd use Concourse in real-world scenarios.
Flight School: an interactive example of testing and deploying a Rails app
Versioned S3 Artifacts: a demonstration of how to semantically version and publish a product
You may also want to just dive right in to some living, breathing Concourse pipelines. These aren't accompanied by documentation explaining them, but it may be useful just to see some real-world use cases: