The bird is an invisable animal in the Witch's House.
Location
It's find inside a cage on the 5th Floor.
The Witch's House
The bird eats the Greenery that is blocking the way to the Skull Puzzel room and Poisonus Hall. Since it is in a cage you can't get it out. To get it out you need to give the man in the jailcell white pollen. He will then be angry for not having a Jade Pipe and accidently knock over the cage making acces to let the bird out.
In Extra Mode you need to have a Green Candle to burn the rope to let the bird out. You also need to scare it out of the cage with the Green Candle.
Once it has eaten the The Greenery you have acces to the rooms that were covered by The Greenery.
Thoughts
People asume the bird is a crow.