DK stands for Double Knit. I'm honestly not sure the origins of that, but it is thicker than sport and not as thick as worsted weight.
Gauge is typically 5 - 5.5 stitches per inch.
Many DK weight yarns can be used for patterns that call for worsted (Alma, Nightshades, Daylights, Wool+Cotton). Other DK weight yarns work for patterns that call for sportweight (Sami, Manos Silk Blend).