A "house" is essentially a container -- for a person, a family, several families or even a large group with shared interests (think of the term "houses of worship.") In the Bible, a "house" is also a container, but for spiritual things rather than natural things. In various uses a "house" can represent part of the mind, the whole mind, a whole person or even a church. The other nuance to the word "house" is that it is generally used in regards to our affections and desires rather than our thoughts and principles. This makes sense; we tend to engage our thoughts and rationality when we are out in the world doing our work, but when we are inside our houses we are driven most by love for our families and the desire to be good to those we love. So "house" tends to represent the things we want and care about -- which are ultimately the things that define us.

1053. That 'and the bow will be in the cloud' means the state of that man is clear from what has been stated and shown already about the bow in the cloud, that is to say, in the next life a person or soul is known among angels from his sphere; and as often as it pleases the Lord that sphere is represented by means of colours like those of the rainbow, variously according to each person's state as to faith in the Lord and thus respectively as to goods and truths of faith. In the next life colours present themselves to view, which on account of their brilliance and splendour are immensely superior in beauty to colours seen with the eyes on earth. Each colour represents something celestial or spiritual.

[2] Those colours derive from the light in heaven, and from the variegation of spiritual light, as stated above. Indeed angels live in light so bright that the light of the world is in comparison no light at all. The light of heaven in which angels live, compared with the light of the world, is as the light of the sun at midday to the light of a candle that is put out and ceases to give any light at all when the sun rises. In heaven there is celestial light and there is spiritual light. Let me compare the two by saying that celestial light is as the light of the sun, while spiritual light is as the light of the moon. But all manner of variation exists depending on the state of the angel receiving the light. The same applies to colours since they are a product of the light. In the heaven of celestial angels the Lord Himself is the Sun, and in the heaven of spiritual angels the Moon. To people who have no conception of the life which souls lead after death these matters are unbelievable. They are nevertheless completely true.