Heraldic Arms in the SCA
By extension, an "armigerous award" is an award which carries with it one of the three above categories of Arms, as well as the three categories themselves. Many Kingdom awards "carry" an Award of Arms(AoA) or a Grant of Arms(GoA). Patents of Arms are restricted to Society wide Peerages.
"Non-armigerous awards," therefore, are awards which do not carry awards and do not make their bearers armigers.
For the sake of completeness and pedantry, it is worth noting that in the SCA, it is possible to have precedence bearing awards which are nonetheless non-armigerous, placing the person in the order of precedence above those without such awards but below any armigers. Many Baronial Level Awards fall into this category, but Principality Level Award and Kingdom Level Awards may also be non-armigerous, depending on their charter.
It is also worth noting that being entitled to display arms is, in the SCA, entirely distinct from actually having arms to display since the process of registering arms is handled by the College of Heralds while the awards themselves are handled by the individual Kingdoms. Once one's arms have been registered with the College, no one else can display them. One would suppose that one should not dispay one's registered arms until one is or becomes an armiger, but quite frankly, I'm not sure anyone cares - especially since heraldic display tends to improve the recreation and medieval feel.