Generally, doors in the Bible represent the initial desires for good and concepts of truth that introduce us to new levels of love and understanding, and even to the Lord Himself. Since a “house” represents a person’s desires, affections and passions, the door serves to introduce true ideas that can put those desires into action.

In John 10:7, the door signifies the Lord, who is good itself and truth itself. (Arcana Coelestia 2356[2])

In Revelation 3:8; 4:1, the door signifies admission to the arcana of heaven revealed. (Apocalypse Explained 260[2])

The meaning depends on context, of course. For example, references to doorposts and lintels are making a distinction between introductory goods and introductory truths. And, in Sodom, Lot's house had two doors -- an inner one and an outer one. When, in Genesis 19:6, Lot tried to convince the men of Sodom not to attack the angels visiting him, he went outside the inner door, but stayed inside the outer door. There, the outer door represents a desire for good that is resistant to the falsity represented by the men of Sodom; the inner door represents true ideas springing from that desire for good. Someone nurturing a desire for good could be admitted through the first door, but would have to learn the truth about how to express that desire before being admitted through the second.

(References: Genesis 19)

260. Verse 4.1. After these things I saw, signifies the understanding illustrated. This is evident from the signification of "to see" as being to understand. "To see" signifies to understand because the sight of the eye corresponds to the sight of the mind, which is understanding. The correspondence is from this, that as the understanding sees spiritual things, so the sight of the eye sees natural things. Spiritual things are truths from good, and natural things are objects in various forms. Truths from good, which are spiritual things, are seen in heaven as distinctly as objects before the eye, yet with much difference; for these truths are seen intellectually, that is, they are perceived; and the nature of this sight or perception cannot be described by human words; it can be apprehended only so far as this, that it has in it consent and confirmation from the inmost that so it is. There are, indeed, confirming reasons in very great abundance, which present themselves to the intellectual sight as a one, and this one is as it were a conclusion from many particulars. These confirming reasons are in the light of heaven, which is Divine truth or Divine wisdom proceeding from the Lord, and which operate in each angel according to his state of reception. This is the spiritual sight of the understanding. Since with angels this sight operates upon the sight of the eyes, and presents the truths of the understanding in correspondent forms that appear in heaven not unlike the forms in the natural world that are called objects, so "to see," in the sense of the letter of the Word, signifies to understand. (What the appearances in heaven are, and that they correspond to the objects of the interior sight of the angels, see in the work onHeaven and Hell 170-176.)

[2] The expression "to see" and not to understand is used in the Word because the Word in its ultimates is natural, and the natural is the basis on which spiritual things have their foundation; consequently if the Word were spiritual in the letter it would have no basis, thus it would be like a house without a foundation. (On this, also see in the work on Heaven and Hell 303-310.) That in the Word "to see" signifies to understand, is evident from the following passages.

In Isaiah:

Who said to the seers, See not; and to those that have vision, See not for us right things; speak to us smooth things, see illusions (Isaiah 30:10).

In the same:

The eyes of them that see shall not be closed, and the ears of them that hear shall hearken (Isaiah 32:3).

In the same:

Look, ye blind, that ye may behold, seeing great things ye do not keep them (Isaiah 42:18, 20).

In the same:

The priest and the prophet err among the seeing, they stumble in judgment (Isaiah 27:7).

And in other places:

Seeing they see not, and hearing they hear not (Matthew 13:1-15; Mark 4:11-12; 8:17-18Isa. Isaiah 6:9-10; Ezekiel 12:2);

besides very many other instances, that do not need to be quoted, since everyone knows, also from the customary modes of speaking everywhere that "to see" signifies to understand; for it is said "I see that this is so," or "that it is not so," meaning "I understand."

[260 ½]. And behold a door opened in heaven, signifies the arcana of heaven revealed. This is evident from the signification of "door," as meaning admission (of which above, n. 208, here, a looking into, which is admission of the sight; moreover, the sight is admitted into heaven where the sight of the bodily eyes is dimmed, and at the same time the sight of the spirit's eyes is enlightened. By this sight all things seen by the prophets were seen. A "door opened in heaven" here signifies the arcana of heaven revealed, because at such a time things that are in the heavens appear; and before the prophets the things that are arcana of the church appear; here arcana respecting the things that were to take place upon the time of the Last Judgment, none of which have been revealed as yet, and which could not be revealed until the judgment was accomplished, and then only through some one in the world to whom it was granted by the Lord to see them, and to whom was revealed at the same time the spiritual sense of the Word. For all things written in this prophetic book were written respecting the Last Judgment, but by means of representatives and correspondences; for whatever is said by the Lord and is perceived by angels, in coming down is changed into representatives, and is so made to appear before the eyes of angels in the ultimate heavens and before prophetic men when the eyes of their spirit have been opened. From this it can be seen what is meant by "a door opened in heaven. "