What does "Auto packing the repository for optimum performance" mean?

To disable for one project:

cd your_project_dir
git config gc.auto 0

To disable globally:

git config --global gc.auto 0

Short version: it means what it says, and if you just let it finish, all will be well.

During most operations which can potentially increase the number of loose (unpacked) objects in the repository (including pushes), Git invokes git gc --auto. If there are enough loose objects (by default, at least 6700), it will then invoke git repack -d -l to pack them. If there are too many separate packs, it will also repack them into one.

A pack is a delta-compressed single file, containing a large number of objects. It's more efficient to store objects in packs, but it takes time to pack (compress) objects, so Git initially creates loose objects, then packs them in batches now and then, via automatic invocation of git gc --auto.

If you let Git finish repacking, this won't happen again for a while. It can indeed take a while, especially if you have a lot of large binary objects, but if it's triggering, then it's a sign that it will probably drastically reduce the amount of disk space taken by the repo. If you really don't want it to happen, you can change the config parameter gc.auto. If you increase it to something much larger than 6700, it will happen less frequently, but take longer when it does. If you decrease it, it'll still have to do your current repack, but subsequently it will happen more often and finish more quickly. If you set it to 0, it will disable automatic repacking.

See man git-gc (under --auto) and man git-config (under gc.auto) for more information.

While Jefroni is correct that sometimes the auto-packing just needs time to complete, if the auto-packing message persists over multiple days as OP describes, there's a good chance that git's cleanup is missing dangling objects, as described in this question.

To see whether dangling objects are triggering ongoing messages about auto-packing, try running git fsck. If you get a long list of dangling commits, you can clean them with

git gc --prune=now

I usually have to run this on my repo every 2-3 months when the auto-packing message doesn't go away after a single pull.