libgit2
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^"lib" signals that this is a software library.
Something you can use in your own software project.
Also, read the first sentence of the README:
libgit2 is a [..] implementation of the Git core methods provided as a [..] linkable library [..], allowing you to write [..] custom Git applications in any language
=> You can use it to write a Git client or server in the language of your choice (provided your language can make use of C-bindings).
As far as I know, this library is used, amongst others, for Cargo, Rust's package manager.