Like beauty and good, evil isn't an objective feature of universe; it's a subjective judgment of human beings. When we judge things to be morally bad, harmful, or merely disagreeable, we call them evil. Furthermore, when we call something evil, we are also saying that thing shouldn't exist. So, for instance, when we refer to cancer as an evil, we're saying that cancer causes us harm and should thus be eliminated. When we say that rape is evil, we're saying that rape is morally bad and shouldn't exist.
Even though evil doesn't objectively exist, the "Problem of Evil" argument still effectively shows that an omnipotent and omnibenevolent God is a fiction. Just replace the word evil with some milder terms, like harm, pain, suffering, etc.