These two phrases refer to the story of Shadrach, Meshach, and Abednego (in this case "boys" refers to young men) as found in Daniel 3:8-30 (text at web address 1). Members of the court of Nebucchednezzar of Babylon denounced their monotheistic practices. In punishment, the king ordered them cast into a fiery furnace, but they were miraculously protected from harm. The story is frequently referred to by Christian authors to refer proverbially to endurance in the face of persecution.
Azarias, an alternative name for Abednego, appears at alpha 581.