The apostle and his wife spoke at the closing session of BYU's annual Women's Conference, which is co-sponsored by the Relief Society of The Church of Jesus Christ of Latter-day Saints.
Both began their talks with experiences from their childhoods in Germany just after World War II, and expressed gratitude for the light of the gospel that came to them in a time of darkness.
Sister Uchtdorf told the women about missionaries that came to her family shortly after her father's death, when she was just 12.
"How I loved those two young missionaries," she said. "They were angels of glory who brought us the restored gospel. And you are the women who will prepare these young men to serve missions."
Elder Uchtdorf spoke of the strength of the women in his life. He said he will always remember his mother's faith as his family was forced to flee their home as refugees twice in seven years.
"My mother instructed us to only take warm clothes and food, but no other possessions," he said. "We were not members of the church at the time, but it is interesting that she took most of our family records and pictures."
Elder Uchtdorf said the difficult times his family experienced during and after the war ultimately brought them to the gospel.
"Some of my memories of these days are of darkness and cold, but with the help of God, we were moved into days where a light was shining forth to all who came out of that darkness and coldness and were willing to accept the Savior," he said.
Elder Uchtdorf's grandmother introduced his family to the church after she accepted the invitation of a single, elderly sister to attend a church meeting.
"This act of kindness might seem to you small, but it changed our lives forever," he said of the woman's invitation. "The gospel lighted up our lives."
He credited his mother, grandmother and mother-in-law with laying the foundation for his faith.
"They went before and ventured into new spiritual territory," he said. "They had faith. They related love to a little boy even in times of despair, darkness and coldness. The light of the gospel, bright as the sun, lighted up their lives, and in return the warmth of their love helped me to feel secure and well-marked in the principles of the gospel."
Elder Uchtdorf said he shared such personal experiences with the audience to illustrate the power of the light of the gospel and to encourage them to use that light to bring blessings into the lives of others.
"The gospel light has the power and purpose to bring blessings into your life and into the lives of those waiting in your path," he said. "You are here to facilitate those blessings. I urge you to bloom where you are planted."
He emphasized that women play a pivotal role in shaping the world and told women never to undervalue themselves.
"My dear sisters, please never underestimate the power of your influence for good," he said. "As President Hinckley said, 'Big things move on small engines.' What you sisters do today will determine how the restored gospel principles can influence the nations of the world tomorrow."
Elder Uchtdorf told women that the Lord has a unique plan for each of them, and they should not try to be what they are not.
"The Lord our God has responsibilities and blessings in store for each of you, individually, far beyond your expectations," he said. "Don't set goals beyond your capacity to achieve. Don't feel guilty, don't compare yourself to others. Do the best that you can, and the Lord will provide the rest. Have faith and confidence in him, and you will see miracles happen in your life and the lives of those you love."
He concluded by offering women assurance that faith will sustain them through whatever they encounter.
"The Lord knows you and loves you and listens to your prayers," he said. "He wants you to succeed in this life and through eternity. If thou art faithful, thou needest not fear. As Joseph Smith said, 'If you live up to your purpose, the angels cannot be restrained from being your associates.' "
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