Environmental degradation can help lead to poverty among people who are already living on the edge of poverty in developing countries. These are people who are already living precarious lives. Environmental degradation makes it harder for them to make their living off the land.
In developing countries, there are often many people who live off the land. They are almost at a subsistence level. They grow food on small farms. They fish in rivers and lakes and oceans. They might rely on the forest for food that they need or for things that they can sell. Environmental degradation takes these things from them.
Imagine, for example, that you are a fisherman in an area near a mine. The mine releases chemicals into the river that you fish or it causes a lot of silt to get into that river. This degrades the habitat of the fish on which you depend and your ability to make a living is decreased. Or imagine that you have a small farm. You and others around you do not know the best farming practices and you deforest the slopes above you for firewood. Then the rains come and there is no forest to break them up and they cause severe erosion. You lose fertile topsoil and your crop yields drop. You end up with less of an ability to feed yourself.
In these sorts of ways, people who make precarious livings off the land can be pushed into poverty by environmental degradation.