Malevolence is a nasty, wicked, evil quality. When you're full of malevolence, you wish harm on others.
Translated from the Latin, malevolence means to wish for bad things — to have ill will. What sets malevolence apart from other kinds of hatefulness is that it implies a deliberate wish for evil. A small child might be mean out of anger or spite, but probably not out of malevolence. Malevolence requires more thought: it's a deeper, more profound kind of badness often associated with devils and villains.