D&C 29

In this revelation from the Lord, we are taught much of the work of the priesthood in the latter days is that  -

"...ye are called to bring to pass the gathering of mine elect; for mine elect hear my voice and harden not their hearts..."  (Doctrine and Covenants | Section 29:7)

The  emphasis and need to gather the elect, the righteous, the saints, "His people", even the House of Israel is found in throughout the scriptures in parables (the parable of the wheat and tares), allegories (the allegory of the olive tree), and prophecies and revelations.  The are to gather to "holy places" for -

"...the decree hath gone forth from the Father that they shall be gathered in unto one place upon the face of this land, to prepare their hearts and be prepared in all things against the day when tribulation and desolation are sent forth upon the wicked."  (Doctrine and Covenants | Section 29:8)

The reason again is found throughout these referenced teachings because -

"...the hour is nigh and the day soon at hand when the earth is ripe; and all the proud and they that do wickedly shall be as stubble; and I will burn them up, saith the Lord of Hosts, that wickedness shall not be upon the earth;
10 For the hour is nigh, and that which was spoken by mine apostles must be fulfilled; for as they spoke so shall it come to pass..."  (Doctrine and Covenants | Section 29:9 - 10)

I strongly believe this burning will literally happen.  But not necessarily with the common thought of fire, but spiritual fire which is the His glory for -

"...the majesty of his glory shall smite them..."  (Book of Mormon | 2 Nephi 12:21)

As the Savior teaches that he twelve apostles will judge the "house of Israel", we learn who are of the house of Israel -

"...to judge the whole house of Israel, even as many as have loved me and kept my commandments, and none else."  (Doctrine and Covenants | Section 29:12)

The House of Israel will then only be those that have loved God and kept His commandments...none else