Git is not a library, it's a program. There are, of course, libraries in many languages for using git[0] from within many other kinds of applications.

Another example of a library would be libjpeg[1] for reading and writing the jpeg image format and dealing with all the different ways the format can be adjusted, which gets incorporated into many applications, for example ImageMagick[2].

Basically, a library consists of code that is intended to be reused by calling it from other code.

[0] It's astonishing how often this gets reinvented. Here are just Python libraries: https://pypi.python.org/pypi?%3Aaction=search&term=git

[1] https://en.wikipedia.org/wiki/Libjpeg

[2] https://en.wikipedia.org/wiki/ImageMagick