We believe that we existed as spirit children of our Heavenly Father before we came to the earth. We call that our pre-existent life. In the pre-existence we learned, developed, grew and were given our freedom to make choices. One of the choices was to come to earth to be learn, grow, develop some more and to be tested. When we come to earth our spirits are given physical bodies. When we die our spirits leave our bodies and go to what is called the Spirit World. After that is the resurrection and then is the possibility to live eternally with our Heavenly Father. 
 
That's just a quick, quick summary. 
 
Here is a weblink with much better explanation: Plan of Salvation

Before we were born, we believe that you, me, and everyone lived in Heaven--which we refer to as "pre-existence" or "pre-mortal Life"--as spirits. Our spiritual bodies looked similar to our physical bodies and we had the same gender. Jesus Christ was/is our eldest brother. 
 
We believe that in the Pre-existence, God, our Father, explained we would come to Earth to receive physical bodies and be tested so we can learn and grow and return to live with Him. Part of the plan was that Jesus Christ would come to Earth and fulfill the atonement. 
 
Lucifer, however, was prideful and did not agree with the plan. He offered his own plan, one that would take away our free agency. He tried to lead away spirits to follow him, and he became Satan. 
 
There was then a war in the Pre-existence. 1/3 of the spirits chose to side with Lucifer, the other 2/3 chose to follow God and His plan. 
 
Because of their rebellion, Lucifer and his follows were not allowed to be born on Earth and gain a body. Instead, they will forever remain spirits. 
 
Everyone who sided with God and Jesus Christ will at some point be born on Earth. That means you and me both chose to follow God and Jesus Christ in the Pre-existence. We were born and gained a body and are being tested so that we can learn and grow and become more Christ-like.

So, if Jesus is our "eldest brother", what about "Jesus Christ, the only Son of God"?? Or is that a Catholic thing?

Just a quick recap: we believe that we are all spirit sons and daughters of our Heavenly Father.  
 
So... As far as Christ being the only Son of God, we believe that He was the only person that was physically begotten by God.