No, they have nothing to do with height (although at 5' I've had my share of jokes over the years!)...
The Shorty Awards are for the best content producers on Twitter--which means they are limited to 140 characters. The first-ever awards received more than 50,000 nominees. The categories range from business to food. Here's a link to more about the awards.
Regardless of whether you use Twitter or not, the sheer numbers highlight the range of ways this new media is being used to share and communicate. Just a little something for Marketers and Management to keep in mind.