Its applicability/accuracy has been questioned.  But, as a thought experiment, I'm going to take it and see where it goes.
As a teenager, I picked up the implication that the couplet referred to our Father in Heaven. After all, at church, when we say God, we almost always are referring to the Father. I think, however, that the couplet takes on a more enlightening meaning if we interpret it instead to refer to Jesus Christ.
The scriptures suddenly made more sense to me when I had the epiphany about 10 years ago that "God" is not the name of the Father. It is a title that is properly applied to either the Father, the Son, or the Holy Spirit. For example, Matthew refers to Christ as "God with us" when writing about the birth of Christ , and Christ refers to Himself as God when discussing His sufferings for our sins. 
So, since Christ can properly be referred to as God, the couplet can be interpreted as follows:
As man is, God once was;Jesus was born as an infant. He grew into a child, then a man. He lived as one of us, subject to the pains and sorrows of life. He had friends and family. He had enemies. He wept. And finally, He died.
As God is, man may become.Christ was risen from the dead, never to die again. He dwells in a glorious realm, free from toil and strife. He can be forever with His loved ones. This can be our eternal reward as well.
 When Gordon B. Hinckley was interviewed on Larry King Live and asked about that couplet, he downplayed its doctrinal significance.
 Matthew 1:23 "Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us."
 Doctrine and Covenants 19:16-18 "For behold, I, God, have suffered these things for all, that they might not suffer if they would repent...Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore..."