What does "sarsaparilla" mean?

Sarsaparilla: (a) Any plant of several tropical American species of Smilax. (b) The bitter mucilaginous roots of such plants, used in medicine and in sirups for soda, etc. Note: The name is also applied to many other plants and their roots, especially to the Aralia nudicaulis, the wild sarsaparilla of the United States.