From the French. Literally: Seek the woman.

Phrase coined by Alexandre Dumas, Sr. in his 1864 Les Mohicans de Paris to indicate that the key to solving a mystery lies in finding a particular woman. Literature both before and after Dumas, especially that of the mystery genre, often includes this trope with surprising effectiveness. Doyle does it. Sayers does it. Even Mark Twain.

Of course, the woman need not actually be a woman. In many cases, the woman being sought in these stories is a man who has cross-dressed to avoid detection. Marjorie Garber calls attention to this practice in her impressive and highly readable Vested Interests: Cross-dressing and Cultural Anxiety. According to Garber, the inability of the detective, and often the reader as well, to recognize cross-dressing as a possibility is the result of a kind of cultural gender blindness. We are incapable of seeing beyond symbolic clothing to the reality of identity.

But I'm getting ahead of myself. Regardless of the biological identity of the woman in question, the important thing to know is that she is sought after, again and again. Why? Why this mysterious woman? What is it we hope to learn? Who is it that we're really looking for?

Many thanks to the Oxford English Dictionary, my help in times of trouble.
Seriously, check out the Garber book. It’s fascinating, and there are lots of pictures.