Leeches have in earlier times been widely used in medicine as a way to remove “bad blood” from patients and to restore the balance of the humours or bodily fluids. After a century and a half in which they fell almost totally out of use, they are returning in some specialised areas, a practice called hirudotherapy, a term formed from hirudo, the Latin name for the little beasts.
So it would be reasonable to assume that that’s where leechcraft comes from. But this is a case where language trips us up. There have been two meanings for leech in English. The other one, long defunct, refers to a doctor or healer, from Old English læce, of Germanic origin. So leechcraft is the art of healing.
Though it’s hardly an everyday word, you stand a good chance of coming across it in modern works of fantasy, to which it lends the necessary feeling of ancientness or otherworldliness, as in the late André Norton’s Wizard’s World of 1989: “But she was renewed in mind and body, feeling as if some leechcraft had been at work during her rest, banishing all ills.”
At one time a dog-leech was a vet, though that term could also serve as a pejorative name for a quack doctor. The ring finger was once called the leech-finger (also the medical finger and physic finger), a translation of Latin digitus medicus. We’re not sure how it got that name, though some writers say it was because the vein in it was believed to communicate directly with the heart and so gave that finger healing properties, for example in mixing ointments. Engagement and wedding rings are traditionally put on that finger of the left hand for the same reason, which is why the vein became known as the vena amoris, literally “vein of love”.