Certain varieties of natural red dye were difficult to obtain and expensive to procure, and therefore signaled high status and wealth. Prior to the 16th century, kermes dye, made from a small insect native to the Mediterranean, was the true red of choice. As it took a huge amount of kermes to achieve the desired vibrant, deep red, it was very, very expensive. Cochineal/carmine red was produced from the tropical New World cochineal insect: the color was much closer to true red than that produced by madder (a plant native to both the Old and New Worlds), required fewer insect bodies to achieve than kermes, and was both more stable and less toxic than the mineral cinnabar. The supply was controlled by the Spanish, as they held the colonies where the insect was found, and was exceedingly profitable for them. (Check out A Perfect Red for more information about the historical cochineal market.)

Likewise, there were other ways to achieve black - oak gall dye, which faded quickly; a dye made from iron, which literally ate the fibers eventually and rusted - but the best was overdyeing a dark indigo with logwood red, another imported New World dyestuff, which was, again, expensive.

And of course there is purple: proper Tyrian purple was found in the secretions of a specific species of sea snail. Said snails required a significant amount of processing to extract the dye in large enough quantities for solidly coloring fabric, so even without sumptuary laws that restricted the color to those of a particular status, you would know that someone in that shade of purple was wealthy.