“He used to make merry over the cleverness of women, but I have not heard him do of it of late. And when he speaks of Irene Adler, or when he refers to her photograph, it is always under the honourable title of the woman.”
The above passage, which was narrated by Watson at the end of the story, wraps up the story by commenting on what Holmes learned – not to take lightly the fairer sex or other opponents, for that matter.
A big theme in the story was the differences between seeing and observing. The differences, which are kind of like the listening versus hearing argument, are tied to comprehension; understanding what you are seeing. Why this section of text was important was because it acknowledges Holmes’ recognition that other people have this ability aside from himself. It also marks a shift in Holmes’ perceptions. Since he is not making merry over the cleverness of women any longer, he is acknowledging that women can have the ability to do such a thing. As for why Adler is the woman, she is the one who changed Holmes’ perceptions and she is the only person who has bested Holmes.