These verses tell us one of the requirements to obtain the highest blessings we can obtain from God--that of returning to His presence, and being with our family eternally. (For a description of the other "heavens" or degrees of glory that exist, and who will be in each, see Doctrine and Covenants 76 verses 50-113)1 In the celestial glory there are three heavens or degrees;2 And in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage];3 And if he does not, he cannot obtain it.4 He may enter into the other, but that is the end of his kingdom; he cannot have an increase.
What exactly is the new and everlasting covenant of marriage? In short, it means that we must be married by the proper authority (by one who holds the priesthood of God, and the sealing power of Elijah). Also, it must be done where God has said--meaning in one of his Holy Temples.
A temple is a Holy place. It is literally the house of God. And because we must be as clean and pure as possible before entering His presence, there are certain requirements that everybody who wants to enter a temple must meet before entering a temple. There are many who think that we do "secret" things inside, and keep people out of the temples to keep those things secret. The truth is, that we would love to have everybody be able to enter the temple. The requirements that must be met to enter a temple are well known. First, you must be committed to keep the commandments of God--to show that you are, you must be a member of the church "in good standing" (i.e. meaning that you are keeping the commandments of God) for at least a year. Then you must obtain a temple recommend from your local bishop and stake president. They give you one of these temple recommends after a brief interview with them, where they ask you some basic questions. The questions relate to your belief in Christ and in the church that He has established. They also ask if you are living the commandments that you have promised to live when you were baptized. The last question they ask is a simple one "Do you believe that you are worthy to enter the temple?" Anybody who meets those requirements can enter the temple of God. (If you want to find out more about what a temple is, where they can be found, and what the purpose of a temple is, you can go to http://www.lds.org/church/temples)
So--with all that background, if you and your spouse wish to obtain the highest blessings that God has for you and your family, you now know what you must do to obtain them--You must be worthy to enter a Temple of God, and be sealed together with your spouse by the power of the priesthood in the temple.
That is not the end though--The sealing in the temple of a man and wife is conditional upon both of them "enduring to the end," meaning that they both promise to continue to keep the commandments of God and keep the promises they have made to each other, and to the Lord all through their lives.
What that means is that the blessings that God promises us are not obtained by meeting the requirements of a simple checklist. We can't simply say "I accept Christ" and be saved. Nor can we say "I have been baptized, so I am now saved" (and then go back to the way our lives were prior to our baptism--we must continue to keep the commandments of God afterwards and through our entire life) The same thing is true with the new and everlasting covenant of marriage--just because we were once able to enter the temple with our spouse and be sealed in the new and everlasting covenant of marriage, does not mean that we automatically receive all the blessings from God that are promised--unless we continue to live our lives in the way that qualified us to enter the temple with our spouse in the first place.
