But what does it mean to “shut the door”?
… to be alone with God in the sanctuary of the human heart, certain preparatory steps must be taken to ensure an authentic encounter with him. Cast out of your heart all sordid desires… greed… superstitions, blasphemies, and evil thoughts. Throw away your resentment – not only those you harbor towards your friends but those for your enemy, too. Take away all those things then enter into your heart, and there you will find joy. .. Enter, purifying everything, lift your eyes to the Lord, and he will hear you.
from St. Augustine Answers 101 Questions on Prayer by Fr. Ermatinger.
The heart, in modern parlance, is understood to be the emotional center of the person; but for antiquity, it was understood to be the locus of the person-ness of the individual: his intellect, his faculties, his will, his sensations, etc. To enter into one’s heart is to enter into the deep recesses of what makes the individual himself. To “shut the door” then is to both excise the heart from vices and worldly impulses, purifying the heart from extrinsic distractions, and to prevent the outer world from reentering to disturb the labor of contemplative prayer. If the labor of prayer is attempted in a cluttered heart, without a shut door, one will find his inner gaze constantly pulled down to created things rather than capable of lifting up to the light of God, which is above. If we are so distracted, one will not be able to distinguish oneself from the world, let alone be able to find God who is above. The light of God hovers above the tumult of the inner sea; it is through reliance upon Him, even amidst the storm of an unclean heart, that one will find the waves calmed at His Word and saltwater blinded eyes murkily beginning to see. For those that have so prepared their hearts, the inner peace will bring them a joy that impels them to enter into prayer.