Unlike the "premium" or "gourmet" designations, "specialty" is a commercial standard by the Specialty Coffee Association of America given to the top 10% of coffees consumed worldwide (more on specialty coffee on their site here). What it means is that coffee should taste better than from most beans you get at the supermarket (well, unless they make it poorly). Looking at the Thrive Farmers Coffee website, a 12-oz bag of coffee starts at around the $10 mark, which means, at the very least, you're getting more expensive coffee than you'd find at most supermarkets (other than Whole Foods or similar chains).
The coffee is a medium roast created specifically for Chick-fil-A and is available at their restaurants nationwide. The flavor profile is described as "notes of caramel and cocoa with a light citrus finish." Price per cup starts at $1.59 for hot coffee.
Chick-fil-A is also adding new iced coffee to their menu. The new offering is cold-brewed, something not offered at any of their major fast food competitors. Cold-brewing is basically steeping coffee grinds for a long time (usually at least 12 hours) at room temperature or colder. It typically results in a smoother cup of coffee than normal brewing methods (but also tends to use up more coffee).
Chick-fil-A's iced coffee also includes two percent milk and pure cane syrup. It's available in original or vanilla and comes in 16-oz or 20-oz servings with prices starting at $2.29 and $2.59, respectively.
