In the 17th century, "pink" meant yellow - or green or brown. In fact, pink did not necessarily describe a particular hue. In those days, pink referred to the way a certain kind of dye, made from a yellow pigment, was fixed to fabric. Old writers mentioned "yellow pink," "green pink," and even "brown pink." But none of these hues were what we'd call "pink pink."
The word used by painters for a light-red hue was "lake." "Lake" meant red, and red included pink.
"Pink" was also the English name for a flower - dianthus - at least as far back as the 16th century. It seems that the modern name for the color pink was derived, much later, from the name of this flower.
The origin of the name "pink" for the dianthus can't be because of its color, then. The flower's name may in turn have came from the verb "to pink." This meant to pierce or make holes in something, producing an effect like lace (as in today's zigzag-cutting pinking shears). The petal-ends of a dianthus are delicately ragged, so it may have been called a "pink" for its form, rather than for its color.
Botanically, there are numerous kinds of pink, such as cheddar pink and Carolina pink. A charming name for one is maiden pink (Dianthus deltoides). It has been surmised that maiden pink was given the name because its pinkness resembled a modest blush.
As a color, pink has accrued all sorts of qualifiers, such as shocking, salmon, rose, pale, and shell, to name a few.
But the word pink has still wider connotations. A "pink slip," for instance, is an unpleasantly pleasant term for being fired. Being "in the pink" means one thing, being "tickled pink" another. Idiomatically, there are hallucinatory pink elephants and filmic Pink Panthers.
Huntsmen's coats are pink (even when they are strong red). Pinkies are little fingers. Australian sheep-shearers call it "pinking" when a sheep is sheared so closely that its skin shows through. A person with left-wing tendencies might insultingly be called a "pinko," as in "not quite red (communist)." Cheerful chaffinches say "pink pink" in Britain, and discontented car engines make a similar sound.
And if you half-shut your eyes and do something with them between a peep and a blink, that is "to pink." Or was. That usage (more's the pity) became obsolete around the start of the 19th century.