I'm Armenian myself and never really understood this.
EDIT: Thanks guys!
It essentially means "descendant of" and is analogous to the English "-son" or the Serbo-Croat "-ić" patronymic suffixes.
So, a descendant of a man called Petros may have a surname called "Petrosyan" or "Petrosian".
Yeah, its like the scottish 'Mc', it means something akin to [descendent] 'of'.