Abarim Publications' online Biblical Greek Dictionary
Purple is the innermost color of the rainbow, and since red is the outermost and signifies beginning (hence words like rudimentary and names like Adam), the color purple denotes completion, particularly of wisdom (i.e. complete enlightenment).
Our noun relates to the verb πορφυρω (porphuro), meaning to heave (of the sea), or to swell or rise in waves that don't break. This verb was also used to describe emotional heaving, which usually came with a reddened face, which in turn resulted in this verb being used to mean to turn red. Hence the much pondered Homeric image of a sea "turning red" or "being flushed with wine" which rather means that it was becoming choppy. But this in turn suggests that Phoenician purple did not so much denote the calm composition of an unmovable sage but rather one who is heaving and breathing heavily and probably making broad gestures.
Where our word technically came from isn't much discussed, but to us here at Abarim Publications it seems that popular reflections might have linked it to (a) the verb πειρω (peiro), to pierce, and its noun πορος (poros), passage, and (2) the verb φυρω (phuro), to mix (possibly comparable to the Hebrew verb בלל, balal, to mix).
Our noun πορφυρα (porphura) occurs 4 times in the New Testament (see full concordance) and from it come the following derivations: