Symbolism, Imagery, Allegory
The fiery furnace is one of the classic images from the Bible, and it represents the victory of people standing up for what they believe, and refusing to bow to oppression.
So, in Daniel 3, three pious Jews named Shadrach, Meshach, and Abednego refuse to worship a giant gold statue that King Nebuchadnezzar set up, choosing to stay loyal to their God. He tosses them into a furnace, they survive, and Nebuchadnezzar not only realizes that they were right, but admits their moral superiority (and the power of their God) in a royal decree.
Talk about a victory for free expression.
The symbol has been spread around, used as an example of great suffering or a time of trial on serious occasions—like in MLK's "Letter from Birmingham" Jail—or on more light-hearted ones, like in Veggie Tales. In the poetry of William Blake, it receives a really complex interpretation, where the three men in the furnace are three parts of the human psyche, and the fourth one is the human imagination which helps preserve and redeem the other parts of the mind. (Dig on that for a minute, why don't you?)
The fourth man in the fire is usually interpreted as being an angel, perhaps the archangel, Michael. His rescuing Shadrach, Meshach, and Abednego also fits in with the greater pattern of Biblical heroes escaping after falling (sometimes literally) into an unpleasant situation. You can see it pretty obviously with Daniel and the Lion's Den, but it happens on other occasions. Joseph gets tossed down a well and left for dead, but makes it out and ends up being incredibly successful. Jesus dies and is put in a tomb, and then resurrects and escapes the confines of death. The tale about Shadrach and his friends is one of the more memorable versions of that story.