Malevolence is the wish to hurt other people — the feeling or the nature of someone who wants harm, not help. It is a noun, so you talk about a person's malevolence, or the malevolence in a look, a plan, or a government. It is a strong, rather careful word. Everyday English more often says they wanted to hurt us, or they were cruel on purpose. Malevolence is colder than a flash of anger: it suggests a lasting will to do harm. Though actually, writers also use it for things that are not people — “the malevolence of the storm” — as if the weather itself meant to hurt, which is a stretch, but you will see it.