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Ob is the Ob(ligatory) reference to what was supposed to be the topic of discussion. It is a term used on mailing lists where an off-topic post was allowed so long as it included at least something on-topic -- an "obligatory" topic-related note, in other words. Such notes usually started with "ob(Topic/Listname)", such as "obDS" on due South lists such as DUESOUTH-L.
"ObFic is more for Fiction lists, short for Obligatory Fiction. Ob-(something) prefacing a portion of a post, designates something which is supposed to drag an off-topic post back on topic. Thus, on a post on a B7 list, where people might have been rambling on about, er, English chocolate bars, someone might stick on the end of their post something like: ObB7: "do you think they have chocolate in the B7 universe, or do you think the Atomic Wars rendered the cacao bean extinct?" Another variation on this is an ObFic post on a fiction list (where discussion or announcements may not be allowed) where someone transforms an announcement into a piece of fanfic. In that case, the entire post is "ObFic"." 
The term dates to 1951; see Science Fiction Citations.
- a 2001 description from Gen Fic Crit