Strictly speaking, Dark Chocolate is chocolate with no milk added, though some chocolate sold as Dark in America may contain milk.
Hershey’s Special Dark® is an example, where the term “dark” is used as part of a “trademark”, rather than a trade description.
In the EU, Dark Chocolate must be a minimum of 35% chocolate liquor; in America, a minimum 15% chocolate liquor is allowed.
That 15% minimum, though, really applies to a broader range of chocolate known as Sweet Chocolate — there is no actual legal definition in America specifically for Dark Chocolate.
Consequently, in effect, Dark Chocolate in America is just chocolate that is darker in colour than “regular” milk chocolate.