Bitcoin has code in its repository that you can run that verifies that it runs as expected. These are split up by unit tests and integration tests, which you can find instructions for how to run here:

https://github.com/bitcoin/bitcoin/tree/master/src/test

https://github.com/bitcoin/bitcoin/tree/master/test

What you're talking about is testing to make sure the bitcoin core software you've downloaded hasn't been tampered with and does in fact come from the core developers. The checksum ensures that the bitcoin core program is exactly the same as what was released. The GPG signature ensures that the file was notarized by a trusted member of the Bitcoin core team.