If I had to guess, I would say it refers to the spindle.
Def. A slender, upright, rotating rod on a spinning frame, roving frame, twister, winder, or similar machine. A bobbin is placed on the spindle to receive the yarn as the spindle is rotated at high speed.
If we're talking about a spinning wheel, I'd guess it's the spinning head, an assembly that includes the flyer (the spindle is a flyer component), bobbin and whorl. I don't know what it'd be on a production machine/spinning frame, but it's probably a head there too.