Stands for "Fresh Of the Boat"; refers to immigrants who once came to America by boat. In its general sense, it may be applied to any immigrant; but recently, there seems to be a consensus to apply it only to Asian immigrants.
Its definition depends on the person who uses the term.
It may used by Americans to designate any Asian person who lives in America. This usage is offensive: it is a epithet used in place of more appropriate term.
It may also used by long established Asian-Americans to identify new Asian immigrants (thus the phrase "Fresh Off"). This usage is offensive: it denotes the new immigrant's inability to adopt American culture and his/her continuing practice of his/her lifestyle from his/her country of origin.
Those F.O.B. kids are shopping in Chinatown