We believe that Jesus Christ is Heavenly Father's Only Begotten Son of the flesh. Mary was his mother. How that happened other than by the power of the Holy Ghost - we don't know and we choose not to speculate. 
 
We are all God's (Heavenly Father) sons and daughters who are begotten from him spiritually. This means that we were created spiritually - in what we call the pre-existence - before we came to earth. More information about this - what we call the Plan of Salvation - can be found here: http://lds.org/ldsorg/v/index.jsp?locale=0&sourceId=45af9daac5d98010VgnVCM1000004d82620a____&vgnextoid=bbd508f54922d010VgnVCM1000004d82620aRCRD

God is our spiritual father our spirits are his children. 
 
Christ is the Only Begotten Son of God. The word Begotten is the past tense of beget which means: to procreate as the father: sire. 
 
Christ is not only the spiritual child of God the Father but God the Father is also sired Christ through the Virgin Mary. Christ is the only man to of even be born in the flesh from God. This is what separates Christ from us. We are born of two mortal parents and inherit mortality through them.  
 
Christ is the son of a mortal mother (Mary) and an immortal father (God). This made Christ inherit a physical body that was immortal but not all powerful and glorified like his Fathers perfected body. Christ walked the Earth as the only immortal man, he could not die unless he willed himself to die. 
 
At the same time he pre-existence memories were covered by the veil of forgetfulness and he could feel pain and suffer.  
 
He grew from grace to grace like all mortal do but given his immortal state he always had the presence of God with him and quickly learned many things that mortal men could never fully understand.  
 
He was transfigured on the mount with Peter, James, and John as witnesses. Here the veil was lifted for Christ and he knew all things from that time forward including his need to lay down his life on Calvary's Cross to atone for our sins.  
 
Christ is the only person to ever of have the veil lifted in his Earth existence, this was possible because he is the Son of God in the Flesh.  
 
 
Being the Only Begotten of God does not make him the only Son of God though. He is the Father of all spirits, we are all his spiritual sons and daughters. Unlike Christ though God is not our physical father, hence Christ if rightly called the Only Begotten Son of God. 
 
Thank you for the Question Joshua! 
 
I hope my answer was sufficient!