What is this knob on our fireplace?
The upper knob is logically the flue control. You really don't want to close off the flue with a roaring fire going. The exhaust gasses need to go somewhere. If not up the flue, then...

The lower knob is logically air intake. It might be from inside the house, or if the insert is externally vented (best) then the air for the fire comes from outside. In either case, shutting that down will dampen the fire, but it will do so gradually as the oxygen in the cavity is depleted. And I don't know if it is designed to completely shut down the incoming air at all.

Personally, if I were the previous owner who installed it, I would have kept the instructions for the insert around. And then when I sold the house, I would have passed on (to the new owner) a whole pile of instruction manuals for every item in the home. Read the manual.