Scarface is the nickname for the 1888-O VAM-1B, one of the most popular Morgan dollar die varieties. A die break on this variety runs through the center of Lady Liberty's cheek, resembling a scar.
The 1888-O VAM-1B comes in a number of stages, most of which are early die state (EDS) coins that are not "Scarface". Most of these EDS stages are worth much less than a true "Scarface". Before you buy a coin that a seller claims is a "Scarface", please do your research so that you know what you're really getting. The link to the VAMview issue that has the article on the Harrison Stages of the 1888-O VAM-1B is http://www.ssdcvams.com/VAMview9.pdf
This photo below shows a true scarface with the die crack across the cheek:
Please note that while the coin shown above is a true Scarface, the coins in the two slabs shown below are not "Scarface". These are the early die state (EDS) of the coin that becomes Scarface. They are collectible but are worth much less than a real Scarface. Even though one of the slabs actually uses the word "Scarface" on the slab, the key is still the word "EDS".
Please click this link for the full VAMworld.com definitions page.