Letting go of something, or someone, isn't as easy as it sounds. It's like picking up pieces of broken vase using bare hands; you don't pick them all up at once because: 1) you can't pick them all at once, and 2) you will hurt yourself by doing so, but instead, we pick them piece by piece.
When we let go of material things, we do it because we no longer need them or it ceased performing its purpose. If it doesn't have a sentimental value to you, you won't think twice giving it up, right?
Aside from material things, personal relationships are also candidate for letting go. May it be friendship, boyfriend-girlfriend relationship, marriage, and death. We let go of a friendship because one party decided to stop making the friendship continue or grow stronger. You let go of a boyfriend-girlfriend relationship and marriage because things are not working out. One of them might have fallen out of love, or priorities might have changed. Worse case is that there's someone else that would immediately take over your place in your other half's life. As for death, it's inevitable; nothing's permanent in this life, as life itself is temporary. Our loved ones may have gone, we may not want them to go but we have to.
We let go of these things because we want to lift the burden that makes our hearts twitch because of the pain it feels whenever we think of what supposedly we are holding on to. Memories, yes. These memories will forever stay in our minds, whether we want them or not, and we select those we want to always remember and overcome the memories we want to be erased. But these memories will not happen again. When we look back on those happy thoughts (or maybe depressing/sad for others), we tend to think, "What if things worked out differently?" or "Maybe I should have done this instead of that in order to save our relationship". Would they even still matter right now? Perhaps yes, if you are in reconciling terms/ civil with the other person. Otherwise maybe not.
Letting go is freeing yourself from the pain you acquire from the abrupt change in your friendship. Letting go is giving more time to your own needs than reminiscing the past. Letting go is giving up holding on to the memories and start making new brighter ones. Letting go is making yourself look forward to new challenges in life instead of pondering if somebody from the past would be disappointed for your actions. Letting go is making new acquaintances and friends rather than waiting for old friends to resurface in front of you. Letting go is giving yourself a total makeover in your outlook on life. Letting go is accepting the passing of your loved ones. Letting go is loving yourself more than you love others.