Natural evil is the sort like hurricanes, epidemics, plagues, and the like. That kind of thing. Both must be tolerated in order for freedom to have any meaning at all. If God were to step in and set aside every hurricane and every virus which plagues us, pretty soon the natural world would lose its predictability and we would be unable to rely upon an orderly nature. The same law of gravity both pulls a fully loaded airplane down from the sky, killing 300 people, and, at the same time, enables us to drive ambulances along roadways to bring people to medical care.
Evil is a result of consistent created order.
In order for human choices to have any meaning, we have to be able to choose bad things. My decision to love you, for example, is utterly without significance unless I also have the ability to hate you. The price of having a Mother Theresa who witness so powerfully to God's love is that we also have to have Josef Stalin and Adolf Hitler who witness to ideological hatred. The natural order is free to do as it will, and the human will is free, too. God seems to put a high prize on freedom.