Okay, first we need a definition of evil that we can all agree upon, so how about:
Intentionally acting in such a way as to increase harm and suffering without remorse
I’m pretty sure most people can agree upon that. Next we need to define the kinds of entities that are capable of committing evil. Moral awareness is an important prerequisite. We cannot classify a lion as evil for killing other animals at any given opportunity because they have no sense of right and wrong. So in order to be able to do evil you need the capacity to be aware of your actions, their consequences and how they affect others. As far as we know humans are the only beings possessing of these traits.
So in order for something to be evil it needs to be carried out by a morally aware being. An event which causes suffering and harm repeatedly, but is not down to the actions and intentions of a morally aware being cannot be classified as evil. This means that natural disasters and diseases etc. are not evil. So far so good.
However, when you throw and all-powerful deity into the mix this is when things get difficult (for the theist at least). God fulfils the requirement of being a morally aware entity, most theists will state that God is the source of moral truth, so clearly such an entity is very aware of their actions and the consequences of them.
The attribute of omnipotence creates a problem which is famously termed ‘the problem of evil’. Let me explain it using malaria as an example; malaria kills thousands of children every single day so there is no doubt that such a thing increases suffering and causes harm to others, however without God malaria is not evil because it is not caused by the actions and decisions of a morally aware entity. On theism this is different.
The theist has two choices when it comes to malaria; either God created it himself, or allowed it to happen. Either way this removes malaria from the context of having not been caused by the actions and intentions of a morally aware entity to one in which it is very much in the hands of a morally aware entity.
If God created malaria then he is evil because he intentionally created something that causes large amounts of pain and suffering, apparently with no remorse. If God allows malaria then this creates problems also; because if God cares about our suffering and wants to relieve it then he should want to use his power to prevent malaria, this gives rise to a contradiction because it’s very apparent that God has done nothing to prevent malaria, so either God does not care about our suffering, or God does care about it, but can do nothing (thus meaning God is not omnipotent).
The problem of evil arises because positing the existence of an omnipotent God removes disasters, diseases and famines etc. from the context of being events with no moral agent behind them, to being ones that do. So the theist must then explain the contradiction between omnipotence and omnibenevolence that arises in this situation. This is, in my opinion, the heart of the problem of evil.