Warning: Wikipedia contains spoilers.
She was reportedly born in New Jersey during the year 1858. She followed a career in opera as a contralto. Notable points of her career included performances in La Scala, Milan, Italy and a term as Prima donna in the Imperial Opera of Warsaw, Poland. Sometime before her 30th year, Irene retired from the operatic stage and moved to London, United Kingdom of Great Britain and Ireland. The reasons for her retirement are not stated in the story. But it must have been a profitable career, to allow her to retire in comfort. Dr. Watson mentions her as being deceased at the time of the story's publication and before reaching her 34th year. The reasons of her death were not stated. However it has been speculated that the reason of both her early retirement and her early demise was a hidden health problem.
On March 20, 1888, according to the story, Wilhelm Gottsreich Sigismond von Ormstein, Grand Duke of Cassel-Felstein and hereditary King of Bohemia (though historically the current King was Franz Joseph of Austria) incognito contacted Sherlock Holmes to secure a photograph from Miss Adler. The Monarch reigned from Prague but c. 1883 and as a Crown Prince, he reportedly paid "a lengthy visit to Warsaw" where he "made the acquaintance of the well-known adventuress, Irene Adler". The two became lovers and Irene had kept a photograph of the two of them. The thirty-year-old King explained to Holmes that he intended to marry Clotilde Lothman von Saxe-Meningen, an unseen character and second daughter of the King of Scandinavia. Irene could well threaten this marriage. It should be noted that Scandinavia was at the time actually divided between the domains of three different Kings:Oscar II of Sweden and Norway, Christian IX of Denmark and Iceland and Alexander III of Russia and Finland.
Using his great skills at disguise, Holmes traced her movements and learned much of her private life; then he set up a faked incident to cause a diversion that would let him discover where the picture was hidden. When he came back to snatch it, he found Miss Adler gone, along with her new husband and the goods, which had been replaced with a letter to Holmes! This was the one person ever to outwit Holmes completely.
Irene Adler is a most interesting sort of character to appear in popular Victorian fiction. At a time when ladies were supposed to be ladies, she had "the face of the most beautiful of women, and the mind of the most resolute of men" according to the King. She had the wit to one-up Sherlock Holmes, and he admired her for it. (One might compare the sincere gratitude shown by Einstein toward anyone who caught and corrected an error of his.) Not only that; as she says in the letter to Holmes, "Male costume is nothing new to me. I often take advantage of the freedom which it gives." Holmes does not blink at the shocking revelation that she goes out into the town disguised as a man.
To be sure, Irene Adler was no lady. Watson starts out by describing her as "of dubious and questionable memory." But she earns Holmes's unbounded admiration, and even the King of Bohemia says, "Would she not have made an admirable queen? Is it not a pity that she was not on my level?"—a sentiment which Holmes treats with no attempt to conceal which of the two he thought to be on a higher level.
For all his eccentricity, Holmes frequently expressed Doyle's own views on life, the universe, and everything. With no hint that the author considers Holmes's reaction to be wrong-headed, Irene Adler exposes some contradictions in Victorian standards and is something of a subversive character.