Daniel makes three vows during the book: one to himself, one with Joel and Thacia to God, and a repetition of the second vow to Jesus. His first is made at the age of eight, when he witnesses his father and uncle crucified: Daniel swears to live his live in pursuit of vengeance, to his dying breath.
"I vowed I would pay them back with my whole life. That I would hate them and fight them and kill them. That's all I live for."
His second vow comes later, as his mind begins to expand; he influences Joel and Thacia to join in his mission, but they move the vow in a different way:
"Then we will make a new vow," [Joel] said. "The three of us together. We'll swear to fight for Israel--for--for--" He hesitated.
"For God's Victory," said Thacia swiftly.
(Speare, The Bronze Bow, Google Books)
The second vow changes Daniel's focus. He is no longer driven by his need for direct revenge, but instead is working towards a freed Israeli nation. Because of this, his mindset towards Rosh changes; Daniel starts to see that Rosh never cared about avenging the dead, but only about enriching himself. Because of this new vow, Daniel's heart and mind are opened to the possibility of leaving his anger behind and embracing love and forgiveness; this is shown directly in his third vow, to live and die for God's victory, which he only understands when he accepts the teachings of Jesus.
The vow of Daniel is something that is referenced at various points throughout the text, but it is particularly highlighted at the end of the story, when Daniel is forced into choosing between his vow of vengeance and hatred against the Romans and then the path that Jesus encourages him to adopt, which is one of love and peace. This is something that reaches a particularly critical point at the end of Chapter 23, when Daniel realises that Jesus is not going to resist the Roman occupation in the way that Daniel and others expected: through an armed uprising resulting in violent bloodshed. When he realises this, Daniel feels betrayed by Jesus and isolated because of his vow. Note how this chapter ends:
There was no friend to fight beside him. There was no leader to follow. There was nothing left to him but his hatred and his vow.
Daniel's vow therefore involves swearing hatred against the Roman occupiers and trying to do everything possible to plan their overthrow. Note the way that this quote couples "hatred" with "vow." It is clear that for Daniel, his vow clearly is linked to the emotion of hatred, and this is something that he is unable initially to see beyond. It is only when he thinks further about the teachings of Jesus that he comes to replace that hatred with love and to relinquish the anger and hatred that lay at the heart of his vow. This of course is demonstrated most strongly when Daniel, at the end of the book, invites Marcus, the Roman soldier who is courting his sister, into his house.