In the 1840s, the polka dance craze was sweeping Britain and America. The pattern is named after the dance - not because the two are in any way linked, but just because many products and fashions were given the name polka as a way of cashing in on the popularity of the dance. There were all manner of polka polka hats, polka jackets, and even polka curtain ties (!). Most of such polka fad names faded as the dance craze passed, leaving "polka dot" - inexplicably - as the sole survivor (besides, of course, the dance itself). Since then the pattern's popularity has risen and waned, but I think you'll agree it's here to stay.
Over the early 20th century polka dot prints appeared sporadically in fashion, never quite disappearing but barely clinging on. Then in 1928 Minnie Mouse bounced out of the Walt Disney animation studios, dressed in a polka dot skirt - perhaps we have her to thank for the polka dot's resurgence in popularity in the 1930s? During the 1940s and '50s, polka dots graced the gowns of celebrities from Marilyn Monroe to Elizabeth Taylor, and was a staple of designer collections. The polka dot dress became a staple for Lucille Ball's wardrobe in I Love Lucy, and polka dots of varying sizes featured in 60s Mod fashions.