How does git commit --amend work, exactly?

Say you just committed "B"

... --- A --- B
              ^
              |
            master
             HEAD

Amending "B" will create a parallel commit which becomes the new branch head.

        +---- B
        |
... --- A --- B'
              ^
              |
            master
             HEAD

B' is the commit resulting from a combination of the changes from B plus the changes you had staged when you issued the git commit --amend.

Assume that you're in a clean working state and that your repository looks as follows:

If you then run

git commit --amend

write a commit message, save and quit your editor, the following happens:

1. Your staging area—which, if you haven't staged any new changes, will be identical to commit f42c5—is used to create a new commit: 31b8e. Its parent(s) will be the same as that (those) of the commit you're amending: f42c5.
2. The master branch reference is moved to point to that new commit (31b8e).
3. The HEAD reference follows master.

Note that the amended commit (f42c5) is now unreachable from any reference in your repository (hence its "transparent" style on my graph). It still lives in your repository's object database, but it will eventually be deleted for good, when Git runs its periodic housekeeping, or if you trigger it explicitly by running git gc (garbage collection).

---

Addendum (based on Jason Baker's comment): Note that, as long as the amended commit, f42c5, still exists in your repository and you have a way of finding out its commit ID (for example, by fishing it out of the master branch's reflog), you can still check it out. Running

git checkout master # just to be sure that master is the current branch
git reset --hard f42c5

or (assuming you haven't, in the meantime, made any new commit on master, reset master, or otherwise moved the master branch reference)

git checkout master # just to be sure that master is the current branch
git reset --hard master@{1}

would put you in the following situation:

But now, commit 31b8e would become unreachable.

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According to my knowledge, amend works thus:

For git commit --amend works the changes to amend must be into the stagging area (SA)

1. It makes git reset -- soft for bring back changes committed in the last commit (commit to amend) to the SA and move the index to previous commit (commit before commit to amend). Everything keep how it was before the git commit command were used.
2. It makes git add with all files to add to new commit (it will be the amended commit). The files to add are those were into the SA before the git reset --soft was landed, and after reset these files are kept in the working directory (WD), so it is necessary add them to the SA for generate the amended commit.
3. It makes a Git commit. It will generate a new commit and hence a new id for the amended commit. For this, git commit --amend should not be used with pushed commits.

If you use --no-edit the comment is reused in the amended commit, else you must introduce a new comment (because it is a new commit and every commit needs a comment).

For more information about the staging area and working directory, see Reset Demystified.