During my study I've found some excellent answers and even some scriptures that use the word meditation. In the Old Testament the Lord commands Joshua to meditate on the scriptures (see Josh. 1:8) and in the New Testament Paul instructs Timothy to: "Meditate upon these things; give thyself wholly to them; that thy profiting may appear to all" (1 Timothy 4:15).
To meditate is to consider, ponder, pray, study, search, think, and reflect upon a concept or principle. I found an excellent Ensign article by Chauncey Riddle who teaches about meditation and prayer:
"The helpmate of mighty prayer is meditation. In meditating, one tries to minimize his involvements with the physical world for a time in order to concentrate on something inner, on ideas and feelings. As a person prays sincerely with the Holy Spirit as his guide, that Spirit will bring to him many thoughts and feelings....There are other great articles and words from our prophets and apostles that teach the power and importance of meditation. I especially like this quote from President David O. McKay:
"Meditation cannot be taught, because it is something personal and private; it is the venturing of the soul into the unknown. But it can be learned by anyone who has the courage to think for himself. A likely initiation to meditation is to ponder the scriptures, the words of the living and the dead prophets of God."1
"We pay too little attention to the value of meditation, a principle of devotion.... Meditation is the language of the soul. It is defined as 'a form of private devotion, or spiritual exercise, consisting in deep, continued reflection on some religious theme.' Meditation is a form of prayer....How have you applied the principle of meditation in your life? What has helped you to develop the ability to more fully meditate and ponder on gospel principles? Please share your ideas, experiences, tips, and tricks with us in the comments.
"Meditation is one of the most secret, most sacred doors through which we pass into the presence of the Lord."2
1. Chauncey C. Riddle, "Prayer," Ensign, Mar 1975, 15.
2. "Chapter 4: Elements of Worship," Teachings of Presidents of the Church: David O. McKay, 29.