Embossing vs. Debossing
Embossing and debossing are two processes that use heat and pressure to create a relief using two etched dies. The paper is pressed between a male (raised) counter-die and a female (recessed) die which creates the embossed effect. The difference between the two is that embossing creates a raised effect while debossing creates an indented impression.
When you have something embossed pressure is applied to the backside of the paper so that the front side will have a raised impression. The image is engraved into metal plates so that your image or text will be raised. Embossing things like business cards is a great way to convey the quality and professionalism of your company.
Debossing is the same basic process but reversed. Instead of applying pressure to the back like in embossing, debossing applies pressure to the front of the paper so that the image or text is pressed down into the paper.
Embossing allows you to create very elegant and sculpted effects by adding a beveled edge or adding multiple layers of etching. However the more elaborate the design the more it's going to cost to create the dies.
Hopefully this answered any questions that you might have had about the differences between embossing and debossing.