"Commit on GitHub" means that this commit was created by GitHub on behalf of this user. This happens when you accept a merge request through the user interface. You literally ask GitHub to create a commit for you.
You can also edit any file through the GitHub interface. See this edit icon:

Such editing will be marked as "Committed on GitHub".
If you look at the details of the commit, you will find that it has two properties : Author and Committer. When they differ from each other, GitHub shows what is in the user interface.
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