What does the word "distaff" refer to?

Distaff is another word for spindle and is traditionally associated with women. (Much as an unmarried woman is still sometimes called a "spinster," especially in the UK).

In the horse word, the "distaff" is the female side of a horse's pedigree. (Many breeders consider the mare to give more to the foal than the stallion). It's most often heard when talking about racehorses.