What is the meaning of the term whole grain?

Graphics and quoted text from: Whole Grains Council

Grains, by definition, have 3 major parts: the germ, the endosperm, and the bran.

Whole grains are those that have all of the parts of the natural seed, or kernel (not including an exterior husk that is generally inedible).

To be called "Whole Grain" the product must still have all of the bran, endosperm and germ that it had when it was in the field, although it can milled, ground, cracked, natural, whatever...as long as it still has all of its parts.

If a food label states that the package contains whole grain, the "whole grain" part of the food inside the package is required to have the same proportions of bran, germ, and endosperm as the harvested kernel does before it is processed.

Refining normally removes the bran and the germ, leaving only the endosperm. Without the bran and germ, about 25% of a grain’s protein is lost, along with at least seventeen key nutrients. Processors add back some vitamins and minerals to enrich refined grains, so refined products still contribute valuable nutrients.

This graphic shows what's lost when wheat is refined, and what's added back when it's "enriched":

Durum is just a variety of wheat. Unless it specifically says "whole wheat" or "whole grain", you can assume that it is refined.

Whole grain refers to any grain where the whole grain is used - that is, the germ (the reproductive part of the seed), the endosperm (the 'flesh' of the grain) and the bran (the skin).

Non whole grain usually means the bran has been removed.

This is really a whole other question, but 'durum wheat' is merely the variety of wheat used to make the pasta.