These finishing techniques are common not only with business cards, but with anything from book covers, to package design, to even wrapping papers. Each of them make your product appealing in its own way, not to mention the combination possibilities are endless!
Embossing is when a page is pressed between two dies and heat and pressure is applied to the back of the page causing an area of the page to rise.
Blind Embossing/Debossing is when a piece is embossed/debossed but no ink is used to add color.
Debossing is the opposite of embossing. The page is pressed between two dies, but instead of pressure to the back of the page, heat and pressure is applied to the front of the page causing an area of the page to recede below the surface of the paper.
Letterpress is a technique similar to debossing, where the letters are covered in ink and are pressed into a sheet of paper causing a sort of debossed effect. When done right, letterpress work can be absolutely beautiful. You can also use a letter press without having the debossed effect, just flat text, such as how books used to be printed. I can go on forever about Letterpresses, but this is just the letterpress basics. I'll save going more in depth perhaps in a later blog post.
Engraving is a technique where an image is carved into a flat sheet of metal, and that sheet of metal is coated in ink and used to print. This technique, as you may know, is used to print currency (as well as many other high security paperwork), because it is nearly impossible to recreate the great level of detail.
Who would want a boring ol' business card when the finishing techniques truly are endless?
Image Sources: http://www.toxel.com/design/2010/06/30/24-creative-die-cut-business-cards/