You can see in this blog post how you can create a patch (collection of changes you want to communicate and apply to another repo)
(picture from the 2008 blog post “Bioruby with git: how would that work?”, published by Jan AERTS)
See also Contributing to Rails with Git as another concrete example.
Nowadays, the GitHub pull request makes it really easy to apply patches on GitHub repos, which is useful when you aren’t a direct contributor (ie you have no right to directly push to a repo).
Actually, fairly recently GitHub introduced “Better Pull Request Emails” to improve the notification of new patches.