Ah yes, "to Sherlock Holmes [Irene Adler] is always the woman" (Bohemia.1.1). Irene Adler only appears in one of Conan Doyle's dozens of stories, but Watson takes care to point out that she remains a significant character in Holmes's personal history nonetheless.
We don't actually find out that much about Irene Adler as a person: she's a contralto singer and a general lady about town who, after some kind of affair with the King of Bohemia, has retired to London. The King of Bohemia hires Holmes to try and recover an unfortunate photograph of the pair – he doesn't want it to reach his soon-to-be-bride before he gets married. While the photograph remains safe, thanks to a promise from Ms. Adler, Holmes does fail to get the picture back from her. In fact, Adler manages to outsmart him entirely, and to sail away from the country with her new husband in tow.
Adler's presence in "A Scandal in Bohemia" is less important for her own sake as a character than for what she allows Conan Doyle to emphasize about Sherlock Holmes. First, given that Holmes never speaks of "the softer passions, save with a gibe and a sneer" (Bohemia.1.1), he seems to assume that women aren't capable of the degree of rational thinking he expects from, say, himself. Adler proves him wrong on the point of women's intelligence, but the larger issue of Holmes's complete lack of interest in romance remains.
As we discuss in Holmes's "Character Analysis" his whole cold fish thing actually makes it easier for Conan Doyle to create a bunch of self-contained, only loosely related episodes for the magazine The Strand to publish. After all, the only emotional continuity in the series focuses on the friendship between Holmes and Watson, a necessary plot point to keep Holmes together with the guy who's copying down his adventures. Adding love interests would totally distract from the mystery plots that are the whole point of the stories.
Thus, Conan Doyle raises the possibility of such a romance – "In [Holmes's] eyes [Adler] eclipses and predominates the whole of her sex" (Bohemia.1.1) – only to destroy it right away and forever by noting, "It was not that he felt any emotion akin to love for Irene Adler" (Bohemia 1.1). And that's that: the formula of cold-fish-Holmes and married-to-a-mostly-invisible-wife-Watson is born on the first page of the first Sherlock Holmes short story.
Second, even though Adler's conduct has not been perfect – after all, she is kind of a blackmailer – Holmes's admiration sets up the unusual moral tone that runs through the remaining stories. Holmes appreciates intelligence, creativity, and vivacity. He's also really chivalrous (read: he emphasizes courtesy towards women).
The King of Bohemia is so rough in his efforts to recover the photograph that, even though he's technically the victim in the story, he seems to us to be the shabbier one by the end of it –"'From what I have seen of the lady, she seems, indeed, to be on a very different level from your majesty,' [says] Holmes coldly" (Bohemia. 3. 35). Holmes's respect for wrongdoer Irene Adler's unconventional honor and grace demonstrates Holmes's highly personal sense of morality and fairness. This sets a definite trend for his later merciful treatment of (admittedly non-female characters) John Turner in "The Boscombe Valley Mystery" and James Ryder in "The Blue Carbuncle."