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.

4691. 'Are you indeed going to reign over us? Or are you indeed going to have dominion over us?' means, Were the concepts in their understandings and the desires in their wills to be made subject to it? This is clear from the meaning of 'reigning' as the subjection of concepts in the understanding, and from the meaning of 'having dominion' as the subjection of desires in the will. This meaning of 'reigning over them' and 'having dominion over them' - being made subject to - is self-evident; but the reason both expressions are used here is that one has regard to concepts in the understanding, the other to desires in the will. It is common in the Word, especially in the prophetical part, for one particular matter to be described by a dual expression. Anyone unaware of the arcanum lying behind this inevitably supposes that it is no more than a repetition made for the sake of emphasis. But that is not the case. Within every single part of the Word the heavenly marriage is present, namely the marriage of truth to good and of good to truth, just as there is a marriage of understanding and will in the human being. One part of a dual expression has reference to truth, the other to good, so that one has to do with the understanding since that is where truth belongs, the other with the will since this is where good belongs. Expressions used in the Word consist of words which in every case mean things like these. This is the arcanum lying behind the use of a dual expression to describe one particular matter, see 683, 793, 801, 2173, 2516, 2712, 4138(end). So that is the case here also with 'reigning over them' and 'having dominion over them'. 'Reigning' has regard to truth which belongs in the understanding, while 'dominion' has regard to good which belongs in the will; also, 'a kingdom' is used in reference to truth, 1672, 2547, and 'dominion' to good, as is also the case in Daniel where again the Lord's Divine Human is the subject,

To Him was given dominion and glory and kingdom, so that all peoples, nations and languages might worship Him. His dominion is an eternal dominion which will not pass away, and His kingdom one that will not perish. Daniel 7:14.

And in David,

Your kingdom is a kingdom to all eternity, and Your dominion to every generation after generation. Psalms 145:13.