An egg's grade refers to it's interior quality and the condition and appearance of the shell.
Higher quality eggs (Grades AA and A) have a large proportion of thick white, which stands up well around a firm, high yolk. These eggs are ideal for all purposes, and are especially good for frying and poaching where appearance is important.
Grade B quality eggs may have a thinner white, which spreads out more. They are good for general cooking and baking where appearance is not important.