Coco Chanel accidentally got sunburnt while visiting the French Riviera. This helped popularize sun tanning.

Tan skin has been in and out of fashion throughout human history. At the beginning of the last century, for example, tan skin was associated with the lower classes, because they spent the whole day working outdoors. Women even used lead-based cosmetics on their skin to artificially whiten it, a practice that could cause lead poisoning!

By the end of the Victorian era, however, the benefits of sun bathing started getting discovered. For example, it was discovered that sun bathing allowed a person to produce vitamin D, which helped cure certain diseases.  By 1913, sunbathing was considered a desirable activity. 

 In the 1920s, however, fashion icon Coco Chanel accidentally got sunburnt while visiting the French Riviera. Her fans went crazy for the darker look and began to tan themselves. There was another 'caramel-skinned' singer in Paris called Josephine Baker whose fans also in love with her darker tone.

After that, tanning was considered to be fashionable, and it has endured until today.  Tanning has become a whole industry, with products to enhance and prevent the skin from becoming darker. There's even things like this product, which is a string designed to allow women to untie their bikini tops and walk around, all to avoid tan lines. 

(Source)