The Collaborative International Dictionary of English v.0.48:

Cayenne \Cay*enne\, n. [From Cayenne, a town and island in
   French Guiana, South America.]
   Cayenne pepper.
   [1913 Webster]

   Cayenne pepper.
   (a) (Bot.) A species of Capsicum (Capsicum frutescens)
       with small and intensely pungent fruit.
   (b) A very pungent spice made by drying and grinding the
       fruits or seeds of several species of the genus
       Capsicum, esp. Capsicum annuum and Capsicum
       Frutescens; -- called also red pepper. It is used
       chiefly as a condiment.
       [1913 Webster]

WordNet (r) 3.0 (2006):

cayenne
    n 1: plant bearing very hot and finely tapering long peppers;
         usually red [syn: cayenne, cayenne pepper, chili
         pepper, chilli pepper, long pepper, jalapeno,
         Capsicum annuum longum]
    2: ground pods and seeds of pungent red peppers of the genus
       Capsicum [syn: cayenne, cayenne pepper, red pepper]
    3: a long and often twisted hot red pepper [syn: cayenne,
       cayenne pepper]