Ok lets say that you collect a box.
"You receive 20 uridium."
Now the bonus box doubler doubles the reward of bonus box doubler. So if you had it, this is what would happen.
Without : You received 20 uridium.
With : You received 40 uridium.
It just doubles the reward of bonus boxes. It's really helpful if you're botting. I became FE Bio in less than a month with doubler. (: