From SFWiki

South of Market Area, often referred to as SoMa, SoMA, or SOMA is the area south of Market Street generally to the east of The Mission District and north of Mission Bay It was formerly a purely industrial area, but in recent years has seen an increased cultural impact. It is now host to a wide range of shops an restaurants. It also is the home of the SFMOMA, and the Museum of The African Diaspora. It also holds the music venues Slim's, The Bottom Of The Hill and the Hotel Utah.

Further Reading & Outside Links

Here is a good article about soma from the New York Times