You would typically want to UNDO/REDO when you commit some changes to git, and realize that the changes need to be removed/reverted. This very common in scenarios for example, when you did a temporary change to some files, and forgot to revert them, then proceeded to adding them to commit accidentally.

Assuming you did some changes and made commits like:

git commit -m "Commit 1 - Some changes to the code"
git commit -m "Commit 2 - Some MORE changes to the code"

1. (UNDO-ing): Revert back the last commit git reset --soft HEAD~
2. Do the changes.
3. Add your files to the staging area git add <filenames or paths> or git add --all
4. (REDO-ing): Do the commit. git commit -c ORIG_HEAD or git commit -C ORIG_HEAD

Now that you know the flow lets understand how this works behind the scenes.

1. Step 1 resets the last commit i.e. "Commit 2 - Some MORE..." back to the "Commit 1 - Some..." commit.
2. In Step 2, you do changes you deem fit to the files.
3. In Step 3, you add the changed files to the staging area either selectively with git add <filenames> or all files with git add --all.
4. In the final step you commit the changes in the staging area.

Note: you can either use -c or -C. The small -c will open an editor for modifying the commit message, in this case it will be Commit 2 - Some MORE.... You can edit the commit message as you want.

Or alternatively you can use caps -C, where git will skip the editor window, and reuse the LAST commit message which again in this case is Commit 2 - Some MORE....

Re-using the "Same" commit message is also known as redoing/recommiting.

To undo a change staged before a commit simply run git reset <file> or git reset to unstage all changes before a commit.

Note: In older versions of git, the commands were git reset HEAD <file> and git reset HEAD respectively. This was changed in Git 1.8.2

You can go back any number of commits by using git reset --soft HEAD~n where you want to undo last n commits.

This article is based on a Stack Overflow question here and here.