Irene Adler being called "the woman" has been a topic of discussion ever since "A Scandal in Bohemia" was published. Critics and readers alike have wondered whether there is more to Sherlock Holmes' feelings towards Miss Adler than meets the eye. The big question is if he merely admires her or did he feel something romantic as well.
There is no real way to answer this with utter certainty, but the story itself doesn't really corroborate the romantic theory. For one, Holmes barely has any contact with Miss Adler long enough to develop any serious feelings. In addition there seems to be no short-term infatuation either. The famous detective is mostly taken aback by her wit and skill, which ends up earning her the honorary title of "the woman".
The reason for it is that Sherlock Holmes possessed one of the brightest minds in the world, along with his brother Mycroft. His chosen profession meant that he often had to deal with other clever people, but he ended up outwitting most of them. That is to say he didn't have many equals, but they were all men. For Irene Adler to fool him was remarkable. Firstly, she didn't do it through seduction, but keen observance. Secondly, women of the era didn't have as many opportunities as men, which made her character even more impressive. For Holmes, she was therefore above all other women, having proved herself to be brilliant and outwitting him. It also shows that while even Holmes wasn't entirely free of prejudices against women, he didn't let pride get in the way of admitting he'd been bested by her. Being called "the woman" means Irene Adler was on a level close to perfection, a person Holmes could truly admire. This is further proved by Doctor Watson mentioning later that after dealing with Irene Adler, Holmes never underestimates a woman's intelligence again.