JOEL - Many critics of the LDS Church love to use this one for great shock value as they try to prove how non-Christian the LDS Church is to their fellow non-LDS Christians:

John: "Did you know those Mormons believe that Jesus is the brother of Satan?!?"
Bill: "OOOOOH! Wow! No I didn't know that!"

In order to understand where this idea came from in the first place, you need to first understand the LDS concept known as the pre-existance. The spirits of everyone who have lived, are living, or who will live on this earth originate from a sphere of existence known as the the premortal life. All spirits, including Satan's, were born of our Heavenly Father and Mother before this world and universe were organized. We existed with them, waiting for the time when we could come down to earth and gain a body for our spirits and continue on our path towards eternal life.
The name Lucifer means "light bearer" in Latin and is a translation of the Hebrew Heylel ben Shakhar, which means "herald son of dawn" or "morning star." He was also called "son of the morning" by Isaiah(Isa. 14:12). All these titles imply that he must have originally been someone of importance in God's eyes. But Satan and his fellow spirits, who were also born spiritually of our heavenly parents, rebeled against God and were cast down to earth, never to receive a body.
The prophet Isaiah (Isa. 14:12-15) and John the Revelator (Rev. 12:4-9) both referred to this "war in heaven", as we call it; and Jesus himself spoke of having "beheld Satan as lightning fall from heaven" (Luke 10:17-18).
There are those of other Christian faiths who also accept this concept. Consider what Catholic scholar Giovanni Papini says as he quotes and comments on the writings of the early Christian Lactantius (26-340 AD):

"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 his Father, insured his affection unto himself. This being who from god became bad is called Devil by the Greeks."
[Papini comments:] According to Lactantius, Lucifer would have been nothing less than the brother of the Logos.... The elder spirit, filled with every divine virtue and beloved by God above all other spirits, can easily be recognized as Word, that think that the other Spirit, also endowed with every grace, was the second son of the Father: the future Satan would be, no less, the younger brother of the future Christ. (The Devil [NY:E.P. Dutton & Co., 1954], 81-82; original Lactantius, Divine Institutes II)"

All spirits, both good and bad, both Jesus and Satan, were created by the same heavenly parents, and therefore only in this sense could we all be considered brothers and sisters. This does not mean that we believe that Satan is anything like Jesus or like anyone else on this earth. Just as we see the potential for great goodness and great evil in humans around us, so has there always been such potential among the spirit children (Heb. 12:9) of God who are blessed with liberty to choose God and Christ or to choose evil. Satan chose the greatest evil possible and as a result became a "fallen angel" and a total and complete enemy to God and Christ.