Special effects in the world of publishing is pretty much the bells and whistles added to the book design to make it have a greater appeal to the consumer.
This Rangers Apprentice cover, for example, is printed on a glossy paper, but has an extra shiny layer on the branding element (which is the title of the series.) This extra shininess is "foil" and it is accompanied by an emboss which makes the shield surface and the words stick out of the surface a little bit. I'm sure we're all familiar with embossing.
This holographic effect is pretty cool. It is often accompanied with an emboss and adds a great element of interest to the image.
Just one more example of the many things effects can do to a book cover. This is a crackle effect.
Here are some other bells and whistles that can be a part of the book:
A book box, which is often used as part of a gift set.
Rough cut pages
Pop up books
Touch books
You get the idea. I think that effects open up a whole new dimension of design and illustration When you know that these things will be incorporated it can really effect your vision for the project.