It is a statement that you make right before you make a big assumption. I'm not quite sure on the technicalities of it all but...
6. To take for granted; suppose
6.A point of view or attitude on a certain question
So you are taking for granted, or supposing, on a point of view or attitude on a given subject.
If you say this around your friends, they will think of the nasty word first, but then you can impress them with your superior vocabulary skills.
This was possibly made popular from HBO's Robert Wuhl Assume the Position. Where he talks about things that history books tend to ignore.
"I think it's safe to assume the position, that there was no such thing as a colonial quickie." -Robert Wuhl
a command given during fraternity initiations, military hazing, or B/D(which are really not that different) to the pledge/plebe/gimp
Oh Mistress, I'd do anything to please you.
Of course you will Rummy. Your punishment is 25 lashings. Assume the position!