The palatability of something is its quality of being tasty or acceptable in some other way. When you're baking a cake, its palatability is much more important than the way it looks.
Food is what you probably think of when you hear the word palatability. It usually has to do with the way things taste, and it comes from the word palate, which in turn is rooted in the Latin palatum, or "roof of the mouth." Palatability has evolved to include other qualities in addition to taste: "I question the palatability of a new tax — will it be acceptable to the voters?"