Like Christians anciently, Mormons believe that all human beings are the offspring of God and that He is the Father of our spirits. (See Acts 17:29 and Hebrews 12:9 if you doubt these doctrines to be biblical.) Unlike traditional Christians, we believe that all of us lived in God's presence prior to being born. We were spirit beings at that time, without bodies of flesh and bones. As the spirit sons and daughters of God, we were all brothers and sisters to each other.
Unique among all the sons of God was the one we know as Jesus Christ. Unlike the rest of us, He was with His Father in the beginning. Unlike us, He was perfect in every conceivable way and had all of the divine attributes and qualities His Father had. The shared a unity of will and purpose to such an extent that together, they were known (along with the Holy Ghost) both individually and collectively, as God. Finally, even though we were all the spirit offspring of our Father in Heaven, Jesus Christ was also His Father's "Only Begotten" Son. Under His Father's direction, Jesus Christ created our universe. He was chosen prior to His birth in Bethlehem to be the lamb who would be slain for our sins.
Another of the spirit sons of God was one named Lucifer. He was a proud and rebellious son who sought to exalt himself above his Father and who was cast out of Heaven for attempting to do so. When Lucifer was cast out of Heaven, he was disowned by his Father, and lost his right to ever again be known as a son of God (or a brother to the greatest of God's sons, Jesus Christ). If Jesus and Satan were sons of the same Father, they were spirit brothers, a fact which in no way reflects positively on Satan or negatively on the Savior of the world.
Mormons, incidentally, did not invent this doctrine. Not by a long shot. In the third century, the Christian writer, Lactantius, wrote:
Before creating the world, God produced a spirit like himself, replete with the virtues of the Father. Later He made another, in whom the mark of divine origin was erased, because this one was besmirched by the poison of jealousy and turned therefore from good to evil. He was jealous of his older brother who, remaining united with the Father, insured his affection unto himself. This being who from good became bad is called devil by the Greeks.
I don't think most Mormons actually care one way or the other whether other Christians accept this doctrine or not. They would just like people to stop trying to make it look like something its not -- like Mormons somehow see Jesus Christ and Lucifer as equals, when nothing could possibly be further from the truth.