To me what it means to "keep moving forward" is acknowledging the past and enjoying the great memories that have come, but not dwelling on mistakes or wishing you could go back to good old times. If you keep yourself in the past there is no room for the future. I know of a few people who tend to focus so much in the past that they feel like nothing is going for them or they will never get what they want and so on. With the thinking of "I wish things could be different" or "I wish I could go back," you are only keeping yourself from having great opportunities. It drives people away when you are stuck in the past. What if you thought about life in a different way? Rather then saying "I wish," what if you looked forward and said "I'm excited for whatever comes my way."
Life is full of tests and trials, but they also bring about great adventures. If you don't keep moving forward how can you have great adventures? I know there have been times in my life when I have wished for plenty of things, but I try to keep in mind this simple message"keep moving forward." You can't go back and you can't fix what is already done, but what you can do is keep moving forward and looking towards those great adventures that may come your way.
It's like what President Joseph B. Wirthlin said "Come what may and love it." There's no use in worrying and wishing that things could be different, but what you can do is let those things that come your way become a part of your life and no matter what comes, you love it! You love it, your learn from it and your grow. https://www.lds.org/general-conference/2008/10/come-what-may-and-love-it?lang=eng
It's not to say we won't have those days where you wish things could be different, but it's important not to dwell. Our Heavenly Father doesn't want us to dwell in the past, he doesn't want us to feel like we aren't good enough or we don't deserve what we want. He wants us to be happy and more importantly he wants us to forgive and keep trying, keep moving, keep building up the kingdom of God and keep sharing your light and love, but you can't do that if you are so caught up in the past.
Of course these are just my thoughts and feelings,but for me remembering daily to keep moving forward brings great happiness to me and draws me nearer to my Lord and Savior, Jesus Christ. Looking at each day as a gift and blessing I find more love, more peace, more opportunities to serve and I find that great things do come. It may not always be what I wanted or expected, but they do come when your focus isn't stuck in what could've happened or what your wish would've happen, but rather what can happen and what will. You never know what will happen until you "keep moving forward." :)