SARUMAN: The old world will burn in the fires of industry; the forests will fall; a new order will rise. We will drive the machine of war with the sword and the spear and the iron fists of the orc. We have only to remove those who oppose us.
The old world burning may be a metaphor for change, but it's also totally literal. Saruman is using the trees of Fangorn to fuel his industry of war. "Industry," and "war": two words that we'll need to watch out for as the movie progresses.
PIPPIN: And whose side are you on?
TREEBEARD: Side? I am on nobody's side because nobody's on my side, little orc. Nobody cares for the woods anymore.
Elves and wizards used to walk through Fangorn and speak with the ents, but in the third age they are forgotten, or worse, people are frightened of them. When Aragorn finds that Merry and Pippin have fled into the forest, Gimli asks what madness could have driven them in there. To be fair, these giant talking tree people can be a bit scary.
TREEBEARD: Sounds like orc mischief to me. They come with fire; they come with axes: gnawing, biting, breaking, hacking, burning! Destroyers and usurpers, curse them!
Mischief sounds like an understatement. The orcs are completely destroying the forest and its inhabitants. Saruman keeps talking about the dawn of a new era as his orcs begin to usurp the rightful place of other species that once inhabited Middle-earth.
WORMTONGUE: How? How can fire undo stone? What kind of device could bring down the wall?
Wormtongue cannot fathom the basic explosive science that Saruman has devised. To him, and to most of Middle-earth (maybe with the exception of the dwarves), Saruman's black powder is more like black magic he has conjured up. But it is merely an advancement in technology, one which will bring about the destruction of the world as we know it.
TREEBEARD: There is always smoke rising from Isengard these days… there was a time when Saruman would walk in my woods. But now he has a mind of metal and wheels. He no longer cares for growing things.
Saruman's iron works are the antithesis of thinks that grow. Growing things are living and provide life to the world and their ecosystems. But metal is cold and detached. It only serves to end lives.
THÉODEN: They will break upon this fortress like water on rock. Saruman's hordes will pillage and burn.
Théoden is using this natural imagery to illustrate how strong his defenses are. Helm's Deep has the permanence of a rock that cannot be altered. But maybe he'd rethink this analogy if he was about to happen to Isengard.
The ents break the dam holding back the Angren River, releasing it upon Isengard where it floods Saruman's war-making machinery, toppling and crushing it.
In the end, Saruman's "fires of industry" are quenched by the forces of nature. The natural world will stand the test of time as the schemes of men and wizards are lost and forgotten, at least until Sauron burns a hole in the Ozone.