Jane said she didn't know what it meant.
Answers.com has a few definitions, but I subscribe to my own:
obviously priveliged, with intentional or unintentional airs and graces.
I guess you could say, for example, that all men with moneyed backgrounds, who attended Yale and belong to expensive private clubs are posh.
There are three possible roots for this word.
The earliest is 19th century UK slang. Posh then meant money, specifically a halfpenny, and stemmed from the Romany word pash, meaning half.
Later the word posh was published in an 1890 dictionary of slang, as meaning 'a dandy'. Dandies were foppish, vain, overdressed gentlemen; the designer label yuppies of their time, if not the more moneyed chavs with their bling. A bit Laurence Llewelyn Bowen.
The most popular suggestion, albeit the most modern, is that the word stems from an acronym. Apparently when the really well-heeled folk travelled between the UK and India around 1918, they booked rooms that not only looked out to daylight (the First Class accomodation) but also switched sides of the vessel for each leg of the return trip, to get the view most likely to be broken by occasional sightings of land instead of just sea and more sea. To that end they travelled out to India in a berth to port (the left) and back to England in one to starboard (the right). Port Out, Starboard Home.
(To be completely fair, you probably needed enough cash that you looked like a right dandy, to afford to be so picky.)