Here exceptionally means extremely — so much that it stands out from what you usually see. “She is exceptionally kind” is not “kind, but this is a special case”; it means she is kind to an unusual degree, almost surprisingly so. It likes to sit in front of an adjective: exceptionally good, exceptionally cold, exceptionally difficult. The feeling is a little careful and educated, but not stiff, and people use it in speech as well as writing. Though actually, the same word can also mean “as a special case, not as the rule”: “Exceptionally, the library will stay open on Sunday.” That second use is less common. When it sits before an adjective, read it as “extremely.”