Contemplative prayer is essentially the focus of the heart, mind and will upon God in love. It is an enjoyment of His presence. It is, as Richard Foster puts it, a loving attention toward God. It is a fulfillment of the greatest commandment — to love God with all our heart, mind and soul. It is what used to be called Christian mysticism. It is a communion with God, who dwells in us through Christ, by the Holy Spirit. Isaiah said that God would keep in perfect peace those whose minds are stayed on the Lord (Isaiah 26:3). Contemplative prayer is a way of doing that.
The Christian tradition of contemplative prayer is about letting go of all the thoughts that distract our attention and focus on God. Remember Mary and Martha (Luke 10:38-42). Martha was worried and upset about many things — she had many distracting thoughts that kept her from being with the Lord. But Jesus said that there was only one thing needed, and that Mary had chosen what was better. She let go of the many things that could have worried and distracted her to embrace the only thing that was really needed. She sat at the feet of Jesus and listened to Him, enjoying His presence.
That is what Christian contemplative prayer is about. Not emptying our minds of everything but, rather, letting go of every thought that distracts us from Jesus so that we may hear Him and be with Him. It is taking time to be like Mary in the midst of our Martha moments.
Have you ever read a passage of Scripture — perhaps about the love of God, or His grace, mercy or faithfulness — and then leaned back to think about it for a while? And having thought about it, did it turn into a prayer to the Lord, and you were thanking Him for it. Or perhaps asking Him to reveal it deeper in your heart and in your life, to show it through you as well as to you? And when you finished, did you linger for a little while in His presence and enjoy what He had just revealed to you in that Scripture or spoke to you about it in the quietness of your heart?
That is a contemplative way of prayer.