Follow up question: How related is "Caucasian" to "Caucasus" (as in region and mountains). There's not much in the Wikipedia entry on "Caucasian".

"The History of White People" by Nell Irvin Painter devotes a chapter to this phenomenon, I'll try to summarize it to the best of my ability.

Whiteness basically became attributed to Caucasians (residents of the Caucasus region by the Black Sea) because of the Ottoman slave trade. It was thought that Caucasian women were fair skinned with light hair, which apparently made them desirable as slaves. From the 1600s onward, Christian European writers often described the need for European powers to save these women who were thought to be oppressed by their Muslim owners.

This myth continued into the 18th and 19th century when phrenology was at its peak and race as we know it in the West was being constructed. "Caucasian" was used as a scientific term to describe those with fair skin in the same way that "Mongol" was used to describe all inhabitants of East Asia, and not just the region that is known as Mongolia today.