What does git fsck stand for?

It stands for File System ChecK. The name is taken from the Unix fsck command, which is used to validate a file system.

It was first called:

• fsck-cached (git 0.99), to check the repository for errors
• then fsck-objects (git 0.99.8), in order to report what exactly is wrong with the object, instead of an ambiguous 'bad sha1 file'.
• and finally git fsck (git 1.5.0, January 2007)

It reflects that Git was initially built as a file system, with a graph of nodes and git fsck is presented in this GitHub Training as a file system check which verifies integrity and finds corrupt objects.