If you divide something into three, you produce three thirds. You can classify these thirds as the top third, the middle third, and the bottom third.
In this example, there are a number of quality grades for carcasses. So each carcass is put into a particular grade.
Your text does not say it, but we must assume that there is another procedure for grading carcasses within each grade, and this process determines the best or top 33.3% of the carcasses in each grade. The text then tells about a specific rule which applies to the top third of carcasses in each quality grade (except Prime).