Geoffrey Chaucer wrote his Canterbury Tales in the late 1300s, and they are still widely read today. The characters who "write" the tales told on their pilgrimage to Canterbury are enumerated in the General Prologue, and each tale is befitting the character of the narrator who tells the story. The phrase from your question, "what women want," is central question of "The Wife of Bath's Tale."
The story is simple: in order to save his life, a knight must discover the answer to the question "what do women want." He has no clue, but an old hag of a woman is able to provide him with the correct answer; though his life is spared, he is forced to keep his word and marry the ugly old woman.
The answer to the question is that women want to rule their husbands:
Wommen desiren to have sovereyntee
As wel over hir housbond as hir love,
And for to been in maistrie hym above.
The wife of Bath, as she is known, has been married many times and suggests what women (what she) really wants is...whatever she wants.
Back to the story. After their wedding, the knight is upset about his future with this awful-looking woman; she gives the knight a choice. He can choose to have a wife who is ugly but loyal and good, or he can choose a flirtatious, unfaithful wife who is beautiful (the classic inner beauty versus outer beauty debate). After he ponders for a bit, the knight says he will leave the decision up to her. This is, apparently, exactly what the woman wanted to hear; she has been given the power to choose, and she chooses beautiful and good. They live happily ever after, of course.