According to Chauncey Riddle, there are special code words or word usages in the Book of Mormon which are not culturally transparent to the user of ordinary English. . . . The four major kinds of hidden meanings involve: (1) obscure usages, (2) technical usages, (3) metaphorical/allegorical usages, and (4) double entendres. . . . The phrase "the house of Israel" involves a double entendre. Double entendre is where there is a plain, straight-forward and legitimate ordinary interpretation of a language usage which is underlayed by a second, more significant but abstruse meaning.
One of the most common references in the Book of Mormon is to Israel and the house of Israel. The surface meaning of the name "Israel" is that it is a reference to Jacob, the son of Isaac, the grandson of Abraham, and the father of the twelve tribes. A principal concern of the writers of the Book of Mormon is what had happened, what was happening, and what would happen in the future to the house of Israel, and particularly to their own family, a branch of the house of Israel. In general, Israel is important as a people in the history of the world because it is through Israel that the blessing of all nations by the seed of Abraham will be administered.
The tie to the seed of Abraham gives us a clue to the deeper, more important meaning of the name Israel. First we know that the name is a new name given to one who was a faithful servant of Jehovah. As a new name, it is given of Jehovah, or Christ, as a reward, and to signify a new relationship of the recipient to Christ. If we look at the name "Israel" etymologically, we see that it is purported to come from two roots. One of the roots means "mighty, a prince, one who rules." The other root ["el"] is the Hebrew name for God. The standard references tell us that the name Israel means "he will rule as God," or "he rules as God."
Now it is plain that he who rules or will rule as God is Jehovah, himself, or Jesus Christ. Thus, "Israel," the new name for Jacob is also a name of God himself, even as was Abram's new name (Abraham). The conclusion is that the house of Israel is the house or family of Jehovah, the house of Christ. The children of Israel are thus of two kinds: the seed of the flesh, the literal descendants of Jacob; and the children of the new and everlasting covenant, who are the children of men who have come unto Christ and have become his sons and daughters, his seed (see Mosiah 15:10-11 for example). [Chauncey C. Riddle, "Code Language in the Book of Mormon," F.A.R.M.S., pp. 1-2, 16-18] [See the commentary on the name Abraham -- 1 Nephi 22:9; see also the commentary on the name Jesus -- 2 Nephi 25:19]