Irene Adler is the only woman for Sherlock Holmes!
This paragraph is referring to Irene Adler. Sherlock Holmes is notorious for not being interested in women. However, he was obsessed with Irene Adler, because she was his equal in terms of intelligence. She was also very beautiful. Watson begins the story this way in order to introduce her to the reader, so that we can understand how important she is to Holmes. She is not just an opponent or a girlfriend. She is both a nemesis and a soulmate. Holmes is not an ordinary man, and Adler is not an ordinary woman.
Adler is clever, and basically got the best of Holmes. For this, he holds her in high esteem. This is why she is “the woman.” When he describes her, it is in terms of what others think of her.
"Oh, she has turned all the men's heads down in that part. She is the daintiest thing under a bonnet on this planet. So say the Serpentine-mews, to a man.
Yet, while Watson says Holmes is incapable of love and above it, because he believes in cold, hard calculation, it is clear that he feels something for Irene Adler. Otherwise he would not have been so interested in her. It is more than just academic. Watson’s point when he says that Holmes is “the most perfect reasoning and observing machine that the world has seen,” but no lover, is that Holmes puts himself above all that. Why then, mention her at all? Why call her “the woman” then? No, she means something to him.
“A Scandal in Bohemia” is about Sherlock Holmes trying to get a photograph that would embarrass the King of Bohemia from Irene Adler. He is unable to do so.
Watson ends the tale this way:
And that was how a great scandal threatened to affect the kingdom of Bohemia, and how the best plans of Mr. Sherlock Holmes were beaten by a woman's wit.
Some men would have been upset by this, but Holmes was impressed. He was so impressed that while he never gave a woman thought before, he did then. In fact, when the king comments that Irene is not on his level, Holmes agrees, saying she is far superior!
The main point of this paragraph—and this story—is that Sherlock Holmes actually is a red-blooded man. He is not immune to the wiles of a woman. He is just more of an intellectual. He cares more about a woman’s wit than her body. He loves Irene Adler in his own way. She is the only woman for him. She is the one who got away—literally!