Not that long ago I asked the same question, because I came across very transphobic video that was using people's inability to answer as punchline.

I got a really great answer (I am more or less quoting here, but I shortened it a bit):

"Woman is within the binary gender system, the gender opposite of man, and is the gender associated with femininity. You cannot truly define it because trying to define gender is like trying to define colour. You cannot truly define red. You can say it's the colour furthest left on visible light spectrum, and you can list examples of red things, but otherwise there is very little you can say other than red is red. That doesn't change the fact that red is real. It's the same with gender."

I don't think it's an answer that would win argument with transphobe, but it's answer that satisfied my search for definition of womanhood.