Here's how it's explained in the book:
* The Myth: In Greek mythology, the Moirai (Fates) are three goddesses who weave the threads of life. They control destiny and can cut a thread to end someone's life.
* Percy's Understanding: When Percy is first introduced to the idea, he thinks it means cutting the thread of life – killing someone.
* The True Meaning: Later, Chiron explains that the Moirai "can also cut the thread to sever a tie, to allow someone to break away and follow a new path."
The Significance:
* Percy's Journey: This concept is important because it reflects Percy's journey. He's forced to leave his life behind as a mortal and embrace his destiny as a demigod.
* Breaking Free: Cutting the yarn is a symbol of breaking free from the past and embracing the unknown.
* Choice: It's not about death, but about choosing your own path.
Ultimately, yarn cutting in *Percy Jackson and the Lightning Thief* represents the freedom to make choices and forge a new destiny – something that Percy, as a newly-discovered demigod, must learn to do.