Mormons use this expression, not as Christians do to express Christ’s divinity, but to refer to their belief that Jesus is the only person Heavenly Father physically begat on earth.
“God was the Father of His fleshly tabernacle, and Mary – a mortal woman and a virgin – was His mother. He is, therefore, the only person born who rightfully deserves the title ‘the Only Begotten Son of God’” (President Ezra Taft Benson, Ensign, April 1991, p. 2).
“We believe that he came into the world, born of Mary, literally and actually, as we are born of our mothers; that he came into the world, born of God the Eternal Father, the Almighty Elohim, literally and actually, as we are born of our earthly fathers” (Bruce R. McConkie, quoted in Sharing the Gospel Course Manual, p. 74).