Purpose means more deliberate, more meaning, more thoughtful, simply more. Like it says in the manual, Preach My Gospel, "He (Heavenly Father) wants to communicate with us, and we can communicate with Him through sincere prayer." (Chapter 3, Lesson 1) The most important word is 'communicate'. We can talk to Heavenly Father. Actually. Sincere Prayer.
President Hinckley said: "The trouble with most of our prayers is that we give them as if we were picking up the telephone and ordering groceries--we place our order and hang up. We need to meditate, contemplate, think of what we are praying about and for and then speak to the Lord as one man speaketh to another." (Gordon B. Hinckley, Teachings of Gordon B. Hinckley, 469).
That is the way to pray with purpose. Then we need to listen.