As a graphic designer, I have to be able to leave something behind or send something to somebody who I'm interviewing with that will catch their eye and remember me. Sometimes, if you can't get an interview, you want to send something just to remind them that you're available. It should include some of your work so they can look at it and know what you're capable of. Another way of using your self-promotional piece, like I mentioned before, is to leave it with the person who just interviewed you. If they interviewed a bunch of people, they will remember you by your piece of work that you left behind. Now, some of you may be confused by this because some people think a self-promotional piece is just a piece of their work that they designed. It CAN be this, but its better to be a little bit more creative so people are more likely to remember you.
Here are some examples.
Now you have to be careful with what you leave behind because it needs to connect to you or the business you're applying to somehow. For example, the first one may have been a designer applying to work for a health company or something along those lines. It needs to click with the person accepting the self-promotional piece. We'll see where I end up with this...