An absence of blue
The assumption of a blue color that we have for the dye fits with the explanation that the color is like that of the sea, which is like the sky, and the sky is similar to the Heavenly Throne, as indicated by the verse that refers to the appearance of a sapphire stone. Though some translations put in the color blue for that, the actual text does not say kachol [blue] but techleth. Here's the text from Menachos 43b:
תניא היה ר' מאיר אומר מה נשתנה תכלת מכל מיני צבעונין מפני שהתכלת דומה לים וים דומה לרקיע ורקיע לכסא הכבוד שנאמר ותחת רגליו כמעשה לבנת הספיר וכעצם השמים לטהר וכתיב כמראה אבן ספיר דמות כסא
Though we tend to have a picture for sky blue as fairly light and might picture a sun-lit sea as in the picture above, it is also possible for the sky to be a darker blue, closer to a dark indigo, which is why the whole color association does not define the shade altogether precisely.
I won't get into the whole discussion or the dyeing process, which was demonstrated there. You can see all that on the tekhelet.com site. Instead I will merely point out something about the color blue.
It is never mentioned explicitly in the Torah or even TaNaCh (though one verse comes close). Though I checked a Concordance myself, I also checked to see what observations were made about it online and found this.
What's particularly fascinating is that this absence of blue in terms of a hue named is not unique to our tradition. There is no mention of that color in Homer either. I wrote about it a few years ago here. I quoted a Radiolab that said:
"Gladstone conducted an exhaustive study of every color reference in The Odyssey and The Iliad. And he found something startling: No blue! "
But while no colors were named in ancient Greek literature, we do see certain colors, like red, white, and yellow are named in the Torah. I do wonder what was it about the ancient world that made it seem unnecessary to name the color blue even when it was obviously seen in the natural world if nothing else.
More details in http://uncommoncontent.blogspot.com/2013/01/you-say-blue-and-they-said.html