One of the trickiest things to wrap one's head around about insects and other arthropods* is also one of the most basic - how they grow. We tend to forget just how different arthropod growth is from our own - I've even known people who work with arthropods regularly to have it slip their mind.
*Other than that a scorpion's anus is at the very end of its tail next to the sting, not under the base of the tail as we chordates might tend to imagine.
For us as vertebrates, growth to maturity is fairly continuous. We start out small, we get steadily bigger. Take a balloon, blow it up, and you've got a fairly good representation of how we grow (yes, I'm massively simplifying things, but bear with me for a moment). Arthropod growth, on the other hand, is more like a series of balloons of different sizes all one inside the other, with the smallest balloon on the outside and the largest balloon at the centre. Start blowing up the balloons, and you'll only be able to blow it up to the size of the smallest balloon. If that smallest balloon breaks open (like an insect moulting its skin), then the balloons can inflate to the size of the second-smallest balloon. And so on and so forth, until you reach the largest size. Instead of growing in size continuously like we do, arthropods grow in steps - an extended period of no obvious increase in size, then a moult followed by a near-instantaneous increase as the animal swells up to fill its new skin, then another period without obvious growth. The change between moults can be drastic, as most obviously shown by the holometabolous insects with their radically different larval and adult stages. Even if the differences in morphology are not so drastic, separate instars (life cycle stages) may occupy distinctly different size ranges, with little or no overlap, and may have very distinct ecologies.
It's not that the arthropod is not growing at all between moults. A new layer of cuticle is being grown inside the old layer, albeit sort of crinkled up so that it can fit. Once the new cuticle has finished growing, the animal enters the pharate ("cloaked") state until the old cuticle is shed to reveal the new. Sometimes, the pharate period will be minimal, and the old cuticle will be shed pretty much as soon as the new one is ready. At other times, though, the pharate period will last for a considerable time. If conditions aren't right for the arthropod to move on to the next stage in its life, its growth may be effectively put on hold. Desert spiders may remain as subadults almost indefinitely, waiting for the rains to come before they moult into mature adults (and if the rains don't come one year, they can wait as subadults until the next). Caterpillars may moult into pupae at the beginning of autumn, but not emerge as butterflies until some time in the next spring when the flowers they feed on are beginning to bloom. If environmental conditions suddenly deteriorate, vertebrates are forced into the awkward position of having to maintain growth despite their reduced food supply. Arthropods, on the other hand, can afford to wait things out.
On the other hand, vertebrates have some liberties that arthropods do not. Most arthropods have a set number of moults in their life cycle, and as a rule they do not reach maturity until the very last moult. The flipside, of course, is that once an arthropod does reach maturity, that's it. They are unable to resume growth should the occasion arise (this is not necessarily a problem because many, if not most, arthropods do not live long as mature adults). [Update: A couple of readers have pointed out that some arthropods do continue to grow and moult after maturity, but this is not the norm. Arthropods being such a mind-bogglingly enormous group, any attempt to make generalisations leaves one bound to make an idiot of oneself.] Contrary to what the cartoons may suggest, little ants do not grow into big ants. Both are fully adult, both are as big as they're going to get. In those ant species that have different sized castes, it's easy to imagine otherwise, but that's simply not the case. Big ants hatched out from their pupa as big ants, little ants hatched out as little ants. Similarly, if the queen of an ant colony were to die, it would not be possible for one of the workers to develop a functional reproductive system and take her place - sterility is a one-way trip.