Embossing is where the image is pushed out of the paper from behind to give an understated elegant look to text or an image. It is basically the same as die stamping without the ink. This can be produced from a copperplate or an embossing die.
Debossing is where the image is pushed into the paper from the front, creating a depressed image on the paper or card stock. These 2 processes are commonly used on monograms and crests.