What it means is a lifetime of peace -when you trust Jesus you know that He will work everything for your good no matter what. If I make a mistake or do something stupid He is always there to forgive me , put me on my feet and draw me back close to His heart, His will and His way. If tragedy befalls me He will be in the midst of my situation bringing unexpected good- I have seen this so many times.
As far as fearful thoughts or dreams I reject them in the Name of Jesus fo the Word of my God declares " God has not given us a spirit of fear but of love, peace and a sound mind"- I simply do not entertain such thoughts for they do not come from my Father- His Word also declares that I should "think (dwell) on things that are of good report"-
King David was a many of many trails and tribulations but he declared
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Psalm62:5 My soul, wait thou only upon God; for my expectation is from him."- I like David have learnrd to expect good things from my Father at all times- as far as your dream it is hard to say but I am willing to bet that most of us have had that type before-
here is a suggestion-
Pray this prayer- Jesus thank you for forgiving my sins be my Lord and Savior, come into my heart and make me new- Jesus give me peace as I sleep , give me Godly dreams and thoughts of You- be Lord of my home and let your peace rest here- thank You for hearing me- Amen