Chromatically, the color pink is light red, made by diluting the color red with white. It has historically been seen as a strong color1, presumably because it stands out strongly against the common palettes found in nature and in our everyday lives. Currently in America and in much of much of Europe the color pink is associated strongly with femininity, and particularly with young, prepubescence girls. This has currently reached the point where you rarely see pink except in conjunction with girls, or during the few holidays that have collected pink as a traditional color; Valentines' day and Easter.
"The generally accepted rule is pink for the boys, and blue for the girls. The reason is that pink, being a more decided and stronger color, is more suitable for the boy, while blue, which is more delicate and dainty, is prettier for the girl."
Ladies' Home Journal, June 1918
Until the 1940s2 the fashion world flip-flopped on who should wear pink; boys, girls, blonds, blue-eyed babies, etc. Individual stores and magazines set their own standards, which were followed or not, as the consumer wished. In the 1940s pink swung back to the girlish end of the spectrum, and this time it stuck. This is probably in large part due to retailers realizing that the stronger the associations between color and sex, the more likely that parents would buy an entirely new wardrobe for a new baby. And it worked; we rarely dress our boys in their older sister's clothes. (You will notice that diapers, blankets, and even cribs and strollers are color-coded now.) In the 1960s and 70s we had a feminist backlash against the color pink for girls, which resulted in decreased sale of pink baby clothes; the Sears, Roebuck catalog did not carry any pink toddler clothes for two years in the 70s. Obviously this did not stick, but the brouhaha over baby colors helped solidify the tradition of 'pink is for girls, blue is for boys'.
Pink's other claim to fame is that it is, along with red, the color of romance, and particularly of Valentine's Day. This is probably because roses have long been associated with love and romance3 since at least the time of the ancient Greeks. Roses were associated with the Greek goddess of love, Aphrodite, and later the corresponding Roman goddess of Venus. Of course, the same is true of the myrtle, apple, and poppy plants, all of which have very nice flowers. Roses probably won out because they are comparatively easy to grow, long lasting, look good in bouquets, and of course, because they accent the crimson heart so nicely. Even so, pink is most commonly used for children's valentines, which traditionally means that either the giver or the receiver will be a young girl.
Pink is closely tied to roses; in most European languages (including both the Germanic languages and the Romance languages) the word for the color pink is some variant the Latin word rosa, meaning rose. English is different because we name the color after a different flower, the pink, a member of the Dianthus family (related to the carnations). The flower, in turn, was most likely named from the verb 'to pink'4, meaning 'to pierce', or 'to make holes in', which is appropriate for a flower with such ragged edges. This probably also comes to us from Latin, by way of pungere meaning to 'to pierce' or 'to prick'. The only other English word from the verb 'to pink' is 'pinking shears'.
It is worth noting that the Komen Foundation has made pink the trademark color for their fight against breast cancer. They started using the Pink Ribbon as a symbol for breast cancer awareness, and now run such programs such as Wear It Pink and Race for The Cure. They are also starting to get propitiatory about the color pink, and have been asking other charities not to use the color pink in their advertising. As the Komen Foundation has already sued to prevent other charities from using the phrase 'for the cure', this has caused some concern. In Canada the Canadian Breast Cancer Foundation claims legal ownership of the pink ribbon as an official trademark, although they have not claimed any specific shade of pink as their own. These organizations, along with National Breast Cancer Awareness Month in the US, has created an additional set of associations with the color pink, reaffirming the feminine associations, but lessening the child-centered focus.
Footnotes:
1. Not only in Europe, but also in Japan, where the color pink was traditionally associated with strength and masculinity. It was (and is) strongly associated with the transient cherry blossoms; the blooming of the cherry trees in the spring represents (among other things) the samurai who is willing to nobly sacrifice his life for his master. As Western culture pushes hot pink for girls around the world, the associations that go with many shades of pink are changing, and the English word has entered the Japanese language as 'Pinku'.
2. More traditionally, both boys and girls were dressed in white, unadorned, easily-bleached dresses. It wasn't until the 1900s that things got fancier, and babies started wearing colors.
3. It is worth noting that roses have also been associated with all kinds of other things, from war to silence to Christ.
4. Some sources claim that the origin might be from the Dutch flower known as the pinken, but the English flower pink was documented in use more than 100 years before the first known appearance of pinken. (1681 vs. ~1570).
References:
Wikipedia: Pink
Smithsonian.com: When Did Girls Start Wearing Pink?.
Theoi.com: Aphrodite
Wiki.answers.com: Why is the Rose a Symbol of Love?
Etymology
Wikipedia: Pink (Flower)