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.

3009. As to the second point - that Messiah, Anointed, or King is the same as Divine Truth - this is clear from very many places in the Word, and has been shown frequently in explanations; as in 1672, 1728, 2015, 2069. The Lord Himself also teaches the same in John,

Pilate said to Jesus, Are you not then a king? Jesus answered, You say it, because I am a King. For this I was born, and for this I have come into the world, to bear witness to the truth. Everyone who is of the truth hears My voice. John 18:37.

From this it is clear that the Divine Truth itself is at the root of the Lord's being called 'the King'. The reason why kings were anointed and consequently called the anointed was that 'the oil' with which they were anointed meant good, 886, 2832. Also the truth, meant by 'king', was derived from good and was accordingly truth grounded in good, so that the kingly office with them represented the Lord as regards Divine Truth which is derived from Divine Good, and so represented the Divine marriage of good within truth, whereas the priestly function represented the Divine marriage of truth within good. The latter is meant by Jesus, the former by Christ.