First off, it is important to understand what it is that we believe in the Lord’s Supper, mainly that on the night in which He was betrayed, our Lord took bread, and when He had given thanks He broke it and gave it to the disciples saying, “Take eat, this is My body which is given for you. This do in remembrance of Me.” In the same manner also, He took the cup after supper, and when He had given thanks, He gave it to them, saying, “Take Drink, this cup is the new testament in my blood, which is she for you for the forgiveness of sins. do this in remembrance of me.”
From this we believe that in, with, and under the bread and the wine of the Lord’s Supper, we receive the very body and blood of our Lord and Savior Jesus Christ, given and shed for the forgiveness of our sins and for the strengthening of our faith. The Lutheran Church–Missouri Synod goes into much more detail on this here.
Now you may be asking, “If the individual receiving the Lord’s Supper receives the forgiveness of sins and the strengthening of their faith, then why do you not allow all people to receive it? It sounds pretty unloving to me!”
Dr. Donald Deffner, states it much better than I can. I puts it this way.
So it is not that a Lutheran congregation wants to bar fellow-saints from the blessings of the Eucharist when they practice Close Communion. It is not that they want to be separatistic, or set themselves up as judges of other men. The practice of Close Communion is prompted by love and is born of the heartfelt conviction, on the basis of Scripture alone, that we must follow Christ’s command. This means refusing the Lord’s Supper to those whose belief is not known to us. It is not showing love to allow a person to do something harmful, even though he may think it is for his own good. It also means if they are members of a Christian body which departs from the full truth of Scripture in some of its doctrines, that we must not minimize the evil of this false teaching by opening our fellowship to any and all Christians who err in the faith.