It needs to be a bare repo because a not bare repo would have a working tree (meaning a specific version of that repo checked out and with files visible).
Each time you are pushing to a non-bare repo, you have no guarantee that its working tree will reflect what you are pushing, since by default said working tree will be untouched.
(Imagine if a push would trigger an update of the working tree: the files would change all of a sudden without any control from users on the receiving end)
That is why it is simpler to have a bare repo as an upstream repo (one you push to): no working tree to manage/update.
See more at “all about “bare” repos — what, why, and how to fix a non-bare push”.
It doesn’t have a checked out tree, so it just does what the “server” notionally does in a centralised VCS — records commits, branches, etc when you push to it, and gives you the latest versions when you clone or pull from it.