Arthropods are members of the largest and most diverse animal phylum. They are invertebrates (they have no spines) with segmented bodies and jointed limbs - hence their name. Their bodies are covered by an exoskeleton or cuticle, basically a tough outer shell made of chitin. Arthropods generally molt their exoskeletons periodically, and because their exoskeletons weaken if very large, the animals themselves cannot reach a huge size; the largest arthropods are aquatic. Arthropods have a pair of limbs per segment. Compared to plankton, say, they are said by biologists to have a complex nervous system, but it's really just a simple brain with a nerve cord and a ganglion in each body segment. In spite of their small brains, arthropods have complex sensory systems involving antennae and feet; they usually breathe through trachea, or small holes in their body, through which oxygen diffuses. Thus their blood doesn't have to carry oxygen and carbon dioxide; still, their simple circulatory systems do carry nutrients and hormones through their bodies.
Beyond those bare bones (or exoskeletons), the arthropods are a diverse lot, and include crustaceans, centipedes, millipedes, insects, arachnids, and a whole lot more.
Trilobites are an important and ancient group of arthropods which are extinct, so the only ones you'll see today are fossilized. However, during the Cambrian and Ordovician periods they were extremely abundant; there were almost 4000 species. They were marine animals with flattened oval bodies in three segments, and ranged in size from planktonic to almost a meter in length.
The three living subphyla of arthropods are Crustacea, Uniramia, and Chelicerata.
The large group which are the crustaceans are made up of animals with two pairs of antennae and two mandibles for food handling. They are mainly aquatic - though some have moved to humid areas near water - and almost all marine. They usually breath through gills. Most crustaceans pass through a series of molts, involving larval stages of develpment. Unlike other arthropods, the cuticle of crustaceans contains calcium. Many crustaceans are shellfish, avidly consumed by humans: shrimps, lobsters, crayfish, crabs; others, like barnacles and tiny plankonic forms, are not eaten by humans, though they of course form an important part of the food chain.
The group Uniramia includes the many-legged: insects and myriapods. The chilopods are centipedes, and are terrestrial. They have two antennae and a trunk region with many segments, each with a pair of legs. They have poison glands at the front of their trunk which they use for paralyzing prior to eating, for they are carnivorous and immobilize their prey - usually smaller arthropods, vicious beasts - with their fangs. The diplopods are millipedes, and are herbivores or scavengers on dead plant material, not bloodthirsty killers like centipedes. Many millipedes produce toxic or just stinky substances to protect themselves from predators. There are 5000 species of centipedes and 8000 species of millipedes; both are spread throughout the globe. There's two smaller more obscure groups in this subphylum, too: the pauropodans and symphylans. The former are small soft-bodied animlas with 9-11 pairs of legs but no trachea and no heart; they live in the soil throughout the world, and there are about 500 known species. The latter are also small, with a dozen pairs of legs, similar in appearance to centipedes, only smaller. They run fast and live off decayed vegetation; there are about 160 species: not that many.
And of course we can't forget the yucky but oh-so-numerous insects. Almost all of the hundreds of thousands of species of insects have one or two pairs of wings on the thorax. They've got antennae and mandibles and compound eyes and a chitonous armour. They are usually terrrestrial and apparently have unique excretory organs known as Malpighian tubules, but I don't want to know much more about insect poo. Insects have many types of adaptation: some eat plant or animal food, others suck up plant sap or animal blood, or lap or swab fruit juice or body fluids; some of them burrow and eat in soil or plant tissues, some run, some jump, some feed while flying. The more primitive insects don't usually change dramatically during their molts; the young often closely resemble their parents in all but size (they're ametabolous). But the least primitive members go through dramatic changes - they are holometabolous, and may be born as wormlike larvae without wings, which only appear after a major metamorphosis. Think butterfly.
The Chelicerata group includes arachnids, sea spiders, and the horseshoe crab; other members are extinct. They have no antennae or jaws; they have chelicera, or pincerlike appendages used for grasping and fragmenting food. Arachnids are the most numerous members of this class, which includes lots of creepy crawly characters like spiders, scorpions, mites, and ticks. They are terrestrial, and their bodies have two segments and (usually) eight legs, the first pair of which are used for killing. They are often capable of injecting their prey with venom to paralyze or kill them. Several members of this class are poisonous to humans. Humans do not, by and large, eat arachnids. There are over 60,000 species of arachnids known.