Mobster \MOB-ster\ , noun;
1. A member of the criminal mob
Dating to 1917, the origin of mobster is mob + -ster with influence from American slang gangster, which dates to 1896. That mob is the criminal version of the word, which dates to the 1680's as "disorderly part of the populace, rabble." It derives from a slang shortening of mobile or mobility ("common people, populace, rabble"), which dates to the 1670's from Latin mobile vulgus ("fickle common people"). Mobile vulgus comes from movere ("to move"), which ultimately derives from the Proto-Indo-European base *meue-.
Mob meaning "gang of criminals working together" is attested from 1839 and originally referred to thieves and pick-pockets. The American English idea of "organized crime" or "Mafia" is first attested in 1927.
There is another obsolete usage of mobster from the 18th century that meant "a member of a mob or crowd, a member of the common people." The later version of mobster has the same etymology as this one, but the two don't seem to be strongly connected because of the influence of gangster. This is perhaps not entirely surprising since the suffix -ster is pretty common.