Scarlet is a deep, red color. It's the color of blood. The idea of the "scarlet thread" comes from a story in the Bible about a woman named Rahab who lived in the city of Jericho (Joshua 2).
Rahab was a woman who lived in a wicked nation which served many false gods. Because of this, the Most High God was going to destroy her nation using His chosen people, the Israelites.
Two Israelite men went to spy on Rahab's nation, looking for ways to destroy them. They hid in Rahab's house while doing their spy work. Rahab knew about their God, and knew He had the power to destroy her nation for their sins.
She also knew God would use the Israelites to do it because they had won many other battles against other nations. So she made the spies promise when they came back to defeat her people, they would not kill her or her family because she had been kind to them and kept them safe in her house.
The two Israelite spies made the promise. But it had a condition on it. The condition was she had to hang a scarlet rope out the window of her house so the Israeli army would know which house was hers.
They also said she and her whole family had to stay inside her house until the war was over so they wouldn't get hurt. They promised as long as the rope was there, everyone inside would be safe.
So Rahab hung the rope out her window. No one in her nation knew what the rope was for. But she and the Israelites did. The scarlet color of the rope represented blood. As long as the blood colored rope was there, they would be saved.
This has become a symbol of the blood of Jesus, which saves us from destruction from eternity in hell. In every book of the Bible we find other symbols of the blood and it's power. That's why we say there is a scarlet thread running through the Bible.
Excerpt permission granted by Kids In Ministry International