The Bronze Bow refers to a passage in one of the Psalms, religious songs and verse attributed to King David. In Psalm 18, the songwriter speaks of having God give him the strength to "fight, and the strength to bend a bow of bronze." This refers to a difficult, perhaps impossible act, which is only achieved through the strength of belief in God and in one's self. To Daniel, the verse comes to represent his entire struggle against the Romans, as he and the others are weak and the Romans are very strong.
"It was you who thought of it, that night -- that the bronze bow might mean some impossible thing -- the thing we could not do alone? I never forgot it. I don't know how to say it, but it came to stand for everything we are working for. For our oath. For the kingdom."
(Speare, The Bronze Bow, Google Books)
The second meaning of the title is explained by Jesus, who desires Daniel to leave his hatred behind and accept the love of God for all creatures. At the very end of the book, Daniel accepts this love and allows the Roman soldier Marcus to see Leah one last time; he has "bent the bronze bow" of hatred with his newfound love of God, self, and those around him.