Apterygote means wingless but not all wingless insects are included in the Apterygota. Some insects are secondarily wingless. This means that they have evolved from winged forms but have lost the wings over time. Lice and fleas are examples of these sorts of insects and an examination of their embryological development shows that they once had wings but no longer need them and so have lost them.
True apterygotes evolved before wings, so do not show any signs of wings in their embryological development. There are four groups of truely wingless insects: Collembola (springtails), Thysanura (firebrats and silverfish) and two small, seldom seen groups, the Protura (coneheads) and the Diplura (bristletails). Some taxonomists have removed these groups from the insects altogether, calling them entognathous hexapods, which means they all have internal mouthparts and six legs and putting them in a class of their own next to the Insecta but still in the Phylum Arthropoda. Older classification systems leave them as a subclass of the Insecta because they are obviously related, due to many shared characteristics, such as having three body parts (head containing sense organs and mouthparts, thorax containing the sex paired and jointed legs, and a segmented abdomen containing .the digestive and reproductive organs) plus a sheddable exoskeleton..
The Protura were so little known when I first studied Invertebrate Zoology that they had no common name. Now they are sometimes referred to as ' coneheads' due to the shape of their front ends. Other than that, they are small, grey or white, six jointed -legged creatures with the requisite three body parts and an exoskeleton to qualify them as as arthropods. They are soil dwellers and as such a part of the soil food chain.
The Diplura are equally invisible to the average observer and also had no common name until recently. Now they are referred to as bristletails, which is their most noteworthy embellishment. They are also small, colourless and live in the soil where they also form part of the food chain. Altogether there are about 800 known speciews of diplurans and about 500bspecies of proturans. Their importance is not in numbers or obviousness, or even as part of the food chain, but arguably, in what they can show us about the first insects and how they evolved.
The Collembola or springtails are also soil dwellers that have never had wings. More people have seen them because when someone turns over a rotten log, these little creatures are often seen springing around using their little tails, which they hook to their abdomen and then release when they are in danger. This propels them up, out and hopefully away from the danger. Not as good as wings, but it obviously works for springtails because they have been around for a long time, presumably as long as the other Apterygota.
The last group are the most well known of the Apterygotes but in negative way. The Thysanura or silverfish have adapted to humans and now inhabit many a home, where they damage books, clothes and other soft furnishings. They aren't as disliked as lice, fleas and mosquitoes but they don't win many popularity contests either. Next time you see them scurrying around, think of the millenia that they have been doing this, since long before we evolved, and give them that credit: they and the other Apterygota are Survivors.