Summary of the article that @bmlyon posted:
As far as I can tell, some dude plagiarized the color names from a paint company and developers used them because they didn't like hex or rgb values. Then, when W3C wrote the CSS spec, they basically said, "Well, if this is what you guys are already using, might as well make it official." A lot of people thought the names were stupid, but W3C stuck to their guns. So don't worry, you're not alone in wondering where the heck those names came from.
Relevant quotes:
"The most substantial release, created by Paul Raveling, came in 1989..."
"In this version, programmers were introduced to the aforementioned “papaya whip” and “lemon chiffon,” as well as other loftily-named hues like “blanched almond” and “peach puff.”
"Raveling drew these names from an unsurprising source: the (now-defunct) paint company Sinclair Paints. It was an arbitrary move; after failing to receive sanctions from the American National Standards Institute (ANSI), which issued standards for Web color properties, Raveling decided to take matters into his own hands."
"By 2001, the World Wide Web Consortium (W3C) published the first working draft of the CSS 3 Color Module..."
"Every browser supported the colors at this point, consequently, the W3C had been using them in compatibility tests. Incorporating the colors into CSS, then, would prevent sites from breaking."