From The Collaborative International Dictionary of English v.0.48:
Cup \Cup\, v. t. [imp. & p. p. Cupped (k[u^]pt); p. pr. & vb. n. Cupping.] 1. To supply with cups of wine. [R.] [1913 Webster]
Cup us, till the world go round. --Shak. [1913 Webster]
2. (Surg.) To apply a cupping apparatus to; to subject to the operation of cupping. See Cupping. [1913 Webster]
3. (Mech.) To make concave or in the form of a cup; as, to cup the end of a screw. [1913 Webster]
From The Collaborative International Dictionary of English v.0.48:
Cupping \Cup"ping\ (k?p"p?ng), n. (Med.) The operation of drawing blood to or from the surface of the person by forming a partial vacuum over the spot. Also, sometimes, a similar operation for drawing pus from an abscess. [1913 Webster]
Cupping glass, a glass cup in which a partial vacuum is produced by heat, in the process of cupping.
Dry cupping, the application of a cupping instrument without scarification, to draw blood to the surface, produce counter irritation, etc.
Wet cupping, the operation of drawing blood by the application of a cupping instrument after scarification. [1913 Webster]