To have a broken heart is to be humble, contrite, repentant, and meek-that is, receptive to the will of God.

I dwell with him that is of a contrite and humble spirit, Isa. 57: 15. Christ offered himself for those who have a broken heart and a contrite spirit, 2 Ne. 2: 7. Offer for sacrifice unto the Lord a broken heart and contrite spirit, 3 Ne. 9: 20 (D&C 59: 8). Only those with broken hearts and contrite spirits are received unto baptism, Moro. 6: 2. Jesus was crucified for the remission of sins unto the contrite heart, D&C 21: 9. He whose spirit is contrite is accepted, D&C 52: 15. The Holy Spirit is promised to those who are contrite, D&C 55: 3. My Spirit is sent forth to enlighten the humble and contrite, D&C 136: 33.