See https://bitcointalk.org/index.php?topic=422021.0 for more detail and more technically correct description.  A simplified version of the transaction looks something like this.

http://i.imgur.com/jDvoJVr.png

I know of at least one case where someone did not understand that change could go back to a different address in their own wallet, they later trashed the wallet with out a recent backup and lost access to that address and many bitcoins of change.  Understand how things work and use backups.