anyway

What is leadership anyway?

What does anyway mean here?

Not enough context, please provide a complete sentence. "Anyway" at the end of a sentence usually means "regardless". It could also be "any way" mis-spelled as one word.
"X was chronically ill at the time but ran for the leadership anyway." (regardless)
"X was not suited to the job in any way" ("at all")

This use of "anyway" is not literal. It is a colloquail way to show the writer's attitude in asking the question, "What is leadership?" It carries an air of impatience, as if the "is" were written in italics. He seems to be saying "Let's define what we mean by leadership before we start talking about it." It's like saying, "Who asked you, anyway?" (with you in italics).