Evgkeni Sampelnikof has posted a nice introduction to defadvice. Emacs is all about having it your way and making it easy to do so. Very often it’s convenient to change the behavior of a built in command and since Emacs has no secrets we can always plunk a copy of the command’s source code into our .emacs file and modify it to produce the desired behavior. Unfortunately, that strategy produces a maintenance problem and adds to the clutter of your (probably overly cluttered) .emacs file.
In many situations, a better way is to use the defadvice macro. It allows you to perform some action before and/or after the command is executed. See Sampelnikof’s post for the details. An excellent example of when you might want to use defadvice was given by Magnar Sveen in his What the .emacs.d!? post about restoring the screen configuration after a call to Magit. That’s a tremendously useful modification to the magit code and I can’t imagine any magit user not wanting it. Happily, it trivial to implement with defadvice.