Something that is appalling is awful or horrible, causing dismay or disgust. It's definitely not appealing.
Like so many things, people have different opinions on what is appalling. Most people find the idea of children living in poverty appalling. Just about everyone thinks a vicious "sport" like dog-fighting is appalling. If you're rich, paying a lot of taxes might be appalling. A football announcer might say that a sloppy play was appalling. Your parents might say the state of your room is appalling. This word can fit just about any situation that disgusts you.