The Collaborative International Dictionary of English v.0.48:

Tyrian \Tyr"i*an\, a. [L. Tyrius, from Tyrus Tyre, Gr. ?.]
   1. Of or pertaining to Tyre or its people.
      [1913 Webster]

   2. Being of the color called Tyrian purple.
      [1913 Webster]

            The bright-eyed perch with fins of Tyrian dye.
                                                  --Pope.
      [1913 Webster]

   Tyrian purple, or Tyrian dye, a celebrated purple dye
      prepared in ancient Tyre from several mollusks, especially
      Ianthina, Murex, and Purpura. See the Note under Purple,
      n., 1, and Purple of mollusca, under Purple, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Tyrian purple
    n 1: a red-purple to deep purple dye obtained from snails or
         made synthetically
    2: a vivid purplish-red color