Status checks are based on external processes, such as continuous integration builds, which run for each push you make to a repository. You can see the pending, passing, or failing state of status checks next to individual commits in your pull request.

Anyone with write permissions to a repository can set the state for any status check in the repository.
You can see the overall state of the last commit to a branch on your repository's branches page or in your repository's list of pull requests.
If status checks are required for a repository, the required status checks must pass before you can merge your branch into the protected branch. For more information, see "About protected branches."