What Does Coldhands Mean When He Says "Your Monster Brandon Stark"

One of the most memorable lines from Coldhands in A Song of Ice and Fire is when he says "Your Monster Brandon Stark" early in A Dance With Dragons. Fans have long wondered what this line is foreshadowing and what being Bran's Monster actually means. Today I want to go over the context this line is said in and explain something I think many people misremember or misinterpret about this line in the effort to figure out what this line could possibly mean for the future of Bran's story in The Winds of Winter.