For Gould ecrever "with the door closed" means that when you have a story to tell, you should write it the way it is in your head, as if you are the only person who should have access to that story at the moment, or that is, you must write with the door closed, in solitude, without interference.
Rewriting "with the door open", however, means that you must edit your story to make it available to others. This means that you must leave your story free for the public, for opinion, for criticism and even for the compliments to come.
These two concepts are important, because they manage to make the writer express and explore all his creativity and narrative capacity in a way that satisfies him, to the point that the writer feels like sharing that story with the world and improving it to achieve that will . This is what makes a good story.