The title of the book refers to a passage in Psalms, the book of songs and verse attribute to King David. In the book, the passage is used to show Daniel's progression from revenge to love; he is unable to get past his own trauma, "bending a bow made of bronze," until he accepts love into his heart. Without love, his anger only pushes up against the immovable force of the Romans, threatening him with breaking instead of bending. In Chapter 7, Daniel decides to use the imagery of the bronze bow as the symbol of his resistance fighters:
"--God is my strong refuge,
and has made my way safe.
He made my feet like hinds' feet,
and set me secure on the heights.
He trains my hands for war,
so that my arms can bend a bow of bronze."
(Speare, The Bronze Bow, Google Books)
The Psalm is number 18, which details praise for God in times of trouble. The narrator describes how God infuses his mind and body with the power to overcome his enemies, and in particular to bend the bronze bow, which is harder than a wooden bow. In theory, a bronze bow would send a more powerful arrow; the symbolism is that a man must be strong enough, either through God or through self, to meet seemingly impossible challenges.