Embossing is when you raise a logo or other image to create a 3D graphic. This raised design is achieved by pushing a metal die into your chosen material from underneath. The raised area can then have foil applied to it for added effect or it can be left unprinted or unfoiled (i.e. known as a blind emboss).
Debossing is the opposite of embossing as you are creating an indent in the material you are using. A metal die is stamped onto the front of the material you are using causing depressions that leave a (debossed) imprint of the image on your chosen material. You can choose to leave the debossing as it is (i.e. known as a blind deboss)
Foil stamping is the application of metallic foil (often gold or silver) or pigment to press a thin layer of foil onto the products material surface with a heated die through heat and pressure.