Converted implies not merely mental acceptance of Jesus and his teachings but also a motivating faith in him and his gospel

“Converted means to turn from one belief or course of action to another. Conversion is a spiritual and moral change. Converted implies not merely mental acceptance of Jesus and his teachings but also a motivating faith in him and his gospel. A faith which works a transformation, an actual change in one’s understanding of life’s meaning and in his allegiance to God in interest, in thought, and in conduct. In one who is really wholly converted, desire for things contrary to the gospel of Jesus Christ has actually died. And substituted therefore is a love of God, with a fixed and controlling determination to keep his commandments.”

- Pres. Marion G. Romney, as quoted by Elder Richard G. Scott Of the Quorum of the Twelve Apostles in "Full Conversion Brings Happiness," Ensign, May 2002, p. 24
http://www.lds.org/ensign/2002/05/full-conversion-brings-happiness?lang=eng