According to Wikipedia's definition, a cathode is "an electrode through which electric current flows out of a polarized electrical device". However, the direction of current flow is purely an arbitrary convention, and is in fact the opposite direction to which electrons flow in a metal conductor. Hence, this definition seems to be a bit lacking.
If the definition is referring to the current carriers, then the definition might be rephrased as "cathode is an electrode through which the charged current carriers flow out" (or "in"?).
How would you define this term clearly and unambiguously? Does the common use of the term "cathode" really reverse when the current carrier is positive, as suggested in the article?
Edit: What actually confuses me is the phrase "Cathode polarity is not always negative". If electrons always flow into the cathode (by way of definition of cathode), this statement implies that the cathode can be at a positive voltage relative to the anode. Can this happen in a "simple" conductor like an electrolyte, or does this require some special circuit?