Old growth trees are trees or forests that are centuries old and not recently cultures.
It's one step short of the German compound noun, and we make it easier to find the fragments...
Pick any point in the past few centuries, and there's going to be something, possibly nowadays always a single word, but not necessarily so even now, that was in a state of flux at the time. The same goes for today.
The poster was correct in asking what a “growth forest” is, because without the hyphen, the phrase parses as an adjective (old) modifying a compound noun.
Though I still lament the loss of the subjunctive form. And diaeresis.
The reason for the distinction is that most of the old growth forests have been clear-cut and the lumber available today is fast-growth farmed lumber. If you compare a 2x4 at Lowe's with a 2x4 out of a 150-year-old house, you'll see that the wood itself is very different even though the species might be the same. The tree the new 2x4 came from was fairly young, while the tree the 150-year-old 2x4 came from was probably centuries old.