An eventuality is a thing that might happen — and people usually say it when they are thinking about a bad or awkward possibility, and getting ready for it. We should plan for every eventuality means: think of the ways this could go wrong, and have an answer. It is a formal, careful, office-and-news word. You would not tell a friend bring a jacket in case of that eventuality; you would say in case it rains, or just in case. Though actually, it does not have to be a disaster — only something that is not certain yet. It sits next to possibility, but it sounds heavier, more like a plan for trouble. Do not mix it with eventually, which means in the end.