Flowering is a euphemism for a girl’s first menstrual period. The blood is the seal of womanhood. It means that she is now fit to be wedded and bedded. 
In the "general Westerosi view," girls may well be wed before their first flowerings, for political reasons, but it would be considered perverse to bed them. And such early weddings, even without sexual intercourse, remain rare. Generally weddings are postponed until the bride has passed from girlhood to maidenhood. 
—Alayne Stone, to Lady Waynwood
—Illyrio Mopatis, on Daenerys Targaryen's suitability as a prospective bride for khal Drogo
For girls, the first flowering is also very significant... and in older traditions, a girl who has flowered is a woman, fit for both wedding and bedding. A girl who has flowered, but not yet attained her sixteenth name day, is in a somewhat ambigious position: part child, part woman. A "maid," in other words. Fertile but innocent, beloved of the singers.
- ↑ A Clash of Kings, Chapter 52, Sansa IV.
- ↑ 2.0 2.1 So Spake Martin: Age of Sexual Relations in Westeros (October 05, 1999)
- ↑ A Feast for Crows, Chapter 23, Alayne I.
- ↑ A Game of Thrones, Chapter 3, Daenerys I.