Terms such as "slain in the Spirit" and "falling under the power" are not found in the Bible. We are not aware of any Scriptures that specifically describe this experience which occurs in some church services, where believers are prayed for and in the process fall to the floor and remain unconscious for a time.
Some call attention to Revelation 1:10-17 which tells how the apostle John fell at the feet of Jesus when he was "in the spirit on the Lord's Day," and saw the glorious revelation of Christ. There was also the transfiguration of Christ, when Peter, James, and John "fell on their face" at the revelation of Christ's glory (Matthew 17:1-8).
Some who have experienced being "slain in the Spirit" say that God used it to minister to them by His Spirit in personal ways. In other instances it has been associated with the new birth, the fullness of the Holy Spirit, spiritual, emotional, or physical healing, or deliverance.
However, whatever one may think about the experience of being "slain in the Spirit," it should not be made an expectation for all believers or be considered a sign of spiritual maturity. In addition, discernment needs to be exercised by mature church leadership since the power of suggestion and mere emotionalism can so easily mimic legitimate spiritual experience.
It is never God's will that we seek spiritual experience for the sake of experience. God's will is that we seek Jesus Himself by faith and in accordance with the Word of God. He is our only source of genuine spiritual experience, satisfaction and fulfillment (Psalm 16:11, Philippians 3:10-14).