I have obtained some of this from dismantling gear and I have no idea what it is used for. I am guessing it is like glimmer and I can buy stuff with it, but I would appreciate if anyone could explain what it is and what it is for.
Bright Dust is indeed a type of currency. It is much more valuable than glimmer and is used to buy items from Eververse. You will get this from items obtained from bright engrams, so they will generally be fore more rare items.