You may find these things in your git repository (.git directory for a repository associated with your working tree, or project.git directory for a public bare repository).
Object store associated with this repository. Usually an object store is self sufficient (i.e. all the objects that are referred to by an object found in it are also found in it), but there are couple of ways to violate it.
You could populate the repository by running a commit walker without -a option. Depending on which options are given, you could have only commit objects without associated blobs and trees this way, for example. A repository with this kind of incomplete object store is not suitable to be published to the outside world but sometimes useful for private repository.
You can be using objects/info/alternates mechanism, or $GIT_ALTERNATE_OBJECT_DIRECTORIES mechanism to borrow objects from other object stores. A repository with this kind of incomplete object store is not suitable to be published for use with dumb transports but otherwise is OK as long as objects/info/alternates points at the right object stores it borrows from.
Traditionally, each object is stored in its own file. They are split into 256 subdirectories using the first two letters from its object name to keep the number of directory entries objects directory itself needs to hold. Objects found here are often called unpacked objects.
Packs (files that store many object in compressed form, along with index files to allow them to be randomly accessed) are found in this directory.
Additional information about the object store is recorded in this directory.
This file is to help dumb transports discover what packs are available in this object store. Whenever a pack is added or removed, git update-server-info should be run to keep this file up-to-date if the repository is published for dumb transports. git repack does this by default.
This file records absolute filesystem paths of alternate object stores that this object store borrows objects from, one pathname per line.
References are stored in subdirectories of this directory. The git prune command knows to keep objects reachable from refs found in this directory and its subdirectories.
records tip-of-the-tree commit objects of branch name
records any object name (not necessarily a commit object, or a tag object that points at a commit object).
A symlink of the form refs/heads/name to point at the current branch, if exists. It does not mean much if the repository is not associated with any working tree (i.e. a bare repository), but a valid git repository must have such a symlink here. It is legal if the named branch name does not (yet) exist.
A slightly deprecated way to store shorthands to be used to specify URL to git fetch, git pull and git push commands is to store a file in branches/name and give name to these commands in place of repository argument.
Hooks are customization scripts used by various git commands. A handful of sample hooks are installed when git init-db is run, but all of them are disabled by default. To enable, they need to be made executable. Read hooks for more details about each hook.
The current index file for the repository. It is usually not found in a bare repository.
Additional information about the repository is recorded in this directory.
This file is to help dumb transports to discover what refs are available in this repository. Whenever you create/delete a new branch or a new tag, git update-server-info should be run to keep this file up-to-date if the repository is published for dumb transports. The git-receive-pack command, which is run on a remote repository when you git push into it, runs hooks/update hook to help you achieve this.
This file records fake commit ancestry information, to pretend the set of parents a commit has is different from how the commit was actually created. One record per line describes a commit and its fake parents by listing their 40-byte hexadecimal object names separated by a space and terminated by a newline.
This file, by convention among Porcelains, stores the exclude pattern list. git status looks at it, but otherwise it is not looked at by any of the core git commands.
Stores shorthands to be used to give URL and default refnames to interact with remote repository to git fetch, git pull and git push commands.