The nine-pointed star symbolizes the nine fruits of the Spirit listed in the Epistle to the Galatians.
This star is sometimes shown with the Latin initials for each of the fruits ( charitas, gaudium, pax, longanimitas, benignitas, bonitus, fides, mansuetudo and continentia) placed within the points.
The nine-pointed star is also the symbol of the Baha'i Faith.
Related Bible Verse
But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness and self-control. Against such things there is no law. (Gal. 5:22, NIV)
The three degrees of glory are described in Section 76 of the Doctrine and Covenants. In the preface to Section 76 in the LDS edition of the Doctrine and Covenants, the following explanatory text is given:
A vision given to Joseph Smith the Prophet and Sidney Rigdon, at Hiram, Ohio, February 16, 1832. Prefacing his record of this vision the Prophet wrote: "Upon my return from Amherst conference, I resumed the translation of the Scriptures. From sundry revelations which had been received, it was apparent that many important points touching the salvation of man had been taken from the Bible, or lost before it was compiled. It appeared self-evident from what truths were left, that if God rewarded every one according to the deeds done in the body, the term 'Heaven,' as intended for the Saints' eternal home, must include more kingdoms than one. Accordingly, while translating St. John's Gospel, myself and Elder Rigdon saw the following vision." It was after the Prophet had translated John 5:29 that this vision was given. 
Assignment to a particular kingdom in the resurrection is contingent upon the faith and works exhibited during mortal life. The LDS Church teaches that these different kingdoms are what Jesus was referring to when he said "[i]n my Father's house are many mansions" (John 14:2).  Additionally, the LDS Church teaches that 1 Corinthians 15:40-41 speaks of these three degrees of glory, comparing them with the glory of the sun, moon, and stars.