What does "architectural" really mean when used to describe building products?
It does not have a consistent meaning, but in the context of building materials/products is usually intended to suggest a higher level of quality or prestige. I think this comes from the suggestion that this particular material might be specified by an architect, who wants a quality project and doesn't care much about price. In contrast, builder-grade products are low-quality, low-price, generally acceptable items available at low cost for builders who want to limit expenses.

In some areas a more specific meaning has evolved - the shingles you point out are an example, where architectural shingles are a class with a typical design (in contrast to cheaper 3-tab shingles).