The Forest of Suicide was a large dark forest located near the Sea of Blood in Hell. It is originally from the book The Divine Comedy. In the book, the forest is described as being a place where people who kill themselves for their sins being too great, and that on occasion demons would come running through the forest wrecking the trees in their path.
As Ryo Utsugi travels to Cocytus, the coldest region of Hell, he passes through the the Forest of Suicide where he remembers what he had read about it in the Divine Comedy. Some of the trees then started to moan and so he runs through the rest of the forest.