What does that mean? Not just sweeping away the past or disregarding the future. As I pondered the phrase, I thought that living now right means focusing on the right things for my current season. That will generally include evaluating the past and making necessary changes, and letting go of things that I cannot change. It means preparing prayerfully for the future but not falling prey to worry. It means choosing the better part in my daily decisions. It especially means having a habit of prayerful gratitude, of paying attention and seeing the Lord's hand in my life and following His guidance.
In short it means exercising faith daily so that I can have peace in the present and hope for the future through the Atonement of Jesus Christ.