What is a fresher grade or an AAA egg?

The grading of eggs is done by "candling" in which a light is shown through the egg to determine the quality of the contents. If the yolk is unbroken and round then it is considered "A" grade and suitable for retail or home use. A grade of AA is given to fresh eggs with a strong shell that can be cooked, unbroken, and made into hard or soft boiled eggs. So, yes, AA is slightly better than a simple A.