What 'checkout' is supposed to mean in 'git checkout' sentence?

To add more to @dnagirl's answer, I think the underlying metaphor used here is a lending library. (Checkout isn't specific to git; it's also used in RCS, which is much older—the oldest source control system, I believe.) One checks out a book at the library, reads it, and then checks it back in. Before computers, I only saw checkout as one word as a noun: the checkout desk. However, it's much easier to render computer commands as single words. Git uses a hyphen in cherry-pick, so I assume they avoided check-out to retain familiarity with RCS and other older systems.

Obviously git differs from the lending library inasmuch as you aren't supposed to change the book you borrowed…

When you checkout files from a versioning software, you take a copy of those files for yourself. If you make changes to your local copy and you don't like them, you can checkout the files again which will copy the repository version over your local version.