Grain free food is any dry dog food that contains no grains such as wheat, corn, oats, rice. It is a basically high protein, low carb dog food. Grains are the number one source of allergies in dogs and are generally used as fillers, so the dogs tend to eat more, absorb less, and poo more than when eating grain free or raw diets.
Even grain free varieties have good an not so good brands. Petco sells good brands as well as Pet Smart, Pet Food Express, and Pet Club. There are online vendors as well. Personally, I think the best kibble out there is Orijen. Others will probably name their favorite. All of the recommendations from people on this forum will be good choices. Lastly, you want to choose a dog food that is rated at least a 4.5 - 5 on the following website http://www.dogfoodadvisor.com
Just search in the name of the food you are considering and you will get a very comprehensive, non-biased review. I can safely tell you that there is absolutely no food that can be purchased at a grocery store that is of any high quality.