Embossing creates a three dimensional effect on paper. Essentially paper is pressed into a piece of shaped metal called a "die”. You can get this effect by placing a penny under a piece of paper and pressing down very hard.You should see the round shape of the coin.
Sometimes an area is embossed to match the printing - such as a logo or company name. Embossing without any printing is called a "blind emboss", which can be more effective because the embossing effect is more visible without ink printed on it.
The more detailed and larger the die, the more expensive it is to create. Dies which have a variety of depths are much more expensive to create and take longer to have done. Once created a die will last for many print runs.