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.

2777. 'On one of the mountains' means Divine love. This is clear from the meaning of 'a mountain' as love, dealt with in 795, 796, 1430, here Divine love since it has reference to the Lord. For the nature of that love, see 1690, 1601 (end), 1789, 1812, 1820, 2077, 2253, 2500, 2572. As it was Divine love from which the Lord fought and overcame in temptations, and from which He sanctified and glorified Himself, Abraham is in this verse told to offer Isaac as a burnt offering 'on one of the mountains' in the land of Moriah. Light is shed on this representative act by the fact that David built an altar, and Solomon the Temple, on Mount Moriah, 2775. For the altar on which burnt offerings and sacrifices were offered, and later the Temple, was the chief representative of the Lord. The fact that the altar was the chief representative of Him may be seen in 921 and is clear in David,

They will bring me to Your holy mountain and to Your dwellings. Then I will go in to the altar or God, to God my exceeding joy. Psalms 43:3-4.

And that 'the Temple' was representative of Him is clear in John,

Jesus said, Destroy this temple and in three days I will raise it up again. He was speaking of the temple of His body. John 2:19, 21.