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 LXX. 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 cited by Christian authors to refer, proverbially, to endurance in the face of persecution.
Azarias, an alternative name for Abednego, appears at alpha 581.