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.

6956. 'In order that they may believe that Jehovah has appeared to you' means in order that they may possess faith with regard to the Lord's Divine Human. This is clear from the meaning of 'believing' as being in possession of faith, not faith that Jehovah or the Lord has been seen with the eyes, but the kind of faith in the Lord that is meant in the spiritual sense; and from the meaning of 'Jehovah has appeared' as the Lord's appearance within His Divine Human, dealt with in 6945, so that 'they may believe that Jehovah has appeared to you' means in order that they may possess faith with regard to the Lord's Divine Human.