The homepage lists lots of things, but does not succinctly specify the core of git-annex. It took me multiple sifts through the pages and a failed attempt at setting it up to discover that, and how it does not do what I currently need.

git-annex allows managing files with git, without checking the file contents into git. While that may seem paradoxical, it is useful when dealing with files larger than git can currently easily handle, whether due to limitations in memory, time, or disk space.

The second sentence does not really help to explain the tool, for me it sounds a lot like git-lfs. My suggestion:

git-annex is a sparse file management tool that tracks files separately from their contents. It enables managing files larger than git can easily handle, whether due to limitations in memory, time, or disk space.

Still not optimal, but feels a little more precise