The Pandora's Box does something special every turn that you own it. More often than not, it does something good; but sometimes it's bad. It might, for instance, increase the industry at the world it is located by one every turn; or it might allow the fleet that's carrying it to travel to worlds that aren't actually connected; or it might self-destruct as soon as it's loaded onto a fleet and take all the ships with it.
The Pandora's Box's behavior is chosen at random at the start of the game, and doesn't change during the game. It always does something, though sometimes it may be hard to figure out precisely what it does. If you come across it and do successfully figure out what it does, you may gain a key advantage in the game. (Then again, you may not.)