A flue damper is a chimney control. It is a variable resistance that slows the velocity of rising gases in the chimney which reduces net draft. It is used to slow the draft of an over drafting chimney.
There are other uses, such as for open door burning with spark screen in place on the double door stoves. This becomes the only control when doors are open.
Antique stoves without door seals that leaked air in making them uncontrollable needed a flue damper to slow the draft, slowing what comes in. Back then, dampers had a metered opening when closed, so coal stoves were ran closed once up to temp.
It is a good thing to have in case you get something stuck in the door, or other failure preventing the door from closing fully. Close damper slowly until smoke starts to roll in at top of door opening. Open enough to evacuate smoke, retaining some heat, and slowing fire.
When starting, if a lot of kindling or cardboard roars up the stack, you can slowly close it until the roar stops. This slows draft, but doesn’t deprive the fire of oxygen like closing the air while starting, when oxygen is needed.
Over-use of flue dampers trying to slow the fire and save wood is a common mistake forming excessive creosote. You’re controlling it correctly using the air intakes.