More detail on the following is available from the git concepts chapter of the user-manual and gitcore-tutorial(7).
A git project normally consists of a working directory with a ".git" subdirectory at the top level. The .git directory contains, among other things, a compressed object database representing the complete history of the project, an "index" file which links that history to the current contents of the working tree, and named pointers into that history such as tags and branch heads.
The object database contains objects of three main types: blobs, which hold file data; trees, which point to blobs and other trees to build up directory hierarchies; and commits, which each reference a single tree and some number of parent commits.
The commit, equivalent to what other systems call a "changeset" or "version", represents a step in the project’s history, and each parent represents an immediately preceding step. Commits with more than one parent represent merges of independent lines of development.
All objects are named by the SHA1 hash of their contents, normally written as a string of 40 hex digits. Such names are globally unique. The entire history leading up to a commit can be vouched for by signing just that commit. A fourth object type, the tag, is provided for this purpose.
When first created, objects are stored in individual files, but for efficiency may later be compressed together into "pack files".
Named pointers called refs mark interesting points in history. A ref may contain the SHA1 name of an object or the name of another ref. Refs with names beginning ref/head/ contain the SHA1 name of the most recent commit (or "head") of a branch under development. SHA1 names of tags of interest are stored under ref/tags/. A special ref named HEAD contains the name of the currently checked-out branch.
The index file is initialized with a list of all paths and, for each path, a blob object and a set of attributes. The blob object represents the contents of the file as of the head of the current branch. The attributes (last modified time, size, etc.) are taken from the corresponding file in the working tree. Subsequent changes to the working tree can be found by comparing these attributes. The index may be updated with new content, and new commits may be created from the content stored in the index.
The index is also capable of storing multiple entries (called "stages") for a given pathname. These stages are used to hold the various unmerged version of a file when a merge is in progress.