What does the term "Out of the Furnace" refer to?

There is a famous term

Out of the furnace and into the fire

This idiom means: from a bad situation into one that is worse, which again is very apt for this film.

In some countries it is changed to from out of the frying pan into the fire but both have the same meaning.

Just to show that this is a used phrase this link shows it in general use

Russell and his younger brother Rodney live in the economically-depressed Rust Belt, and have always dreamed of escaping and finding better lives. But when a cruel twist of fate lands Russell in prison, his brother becomes involved with one of the most violent and ruthless crime rings in the Northeast

As this plot taken from IMDB shows, the two brothers were in a poor state with the economic crisis and it only gets worse.

There's a scene in the film, in which Wesley tells Russell, about his relationship with Russell's former girlfriend Lena: "we may not have that fire, that flame, but what we have, its worth it."

Wesley and Lena's relationship seems indicative of the title's meaning, and of its implications for the film's omnipresent motif of post-Iraq, post-recession American decay. The furnace, like the flame of an intense relationship, refers to what we built/produced (literally and figuratively) as a nation. We may not have that fire, that flame anymore. But what's left, what we have; its worth it. And, most importantly, we don't need to fight to keep what we had. From Vedder's featured song "Release Me," to Wesley's plea to Russell to "let it go" both in reference to Russell's former relationship and (in so many words) in the film's conclusion, and most of all to Rodney's determination to seek out the sort of fight he's grown accustomed to, in lieu of steady work like his brother's; with the recurring suggestion to "let it go," and focus on what remains that is still of importance, Out of the Furnace speaks with resounding clarity. Rather than stay on our high horse, or high in the hills alla Harlan DeGroat, we're implored as American moviegoers to forgo hot-headed brawling battles to maintain waning international preeminence, and settle for what endures, absent such a struggle: to step out of the furnace.