The Kingdom Animalia (=Metazoa) is one of a handful of lineages rooted far back in the branching "tree" that represents the history of life on Earth. This lineage that is composed of those organisms we know as "animals" represents one of the three major origins of multicellularity (the other two large and diverse groups of multicellular organisms are the fungi and the green plants).
It is difficult to list characteristics that apply to all animals, since various branches of the animal tree have undergone a range of significant modifications. However, most animals obtain energy from other organisms. They generally feed on them as predators (killing and eating a prey item); parasites, including herbivores feeding on plants (feeding on their "prey" without killing it, at least not immediately); or detritivores (ingesting tiny bits of decomposing organic material such as fallen leaves). In contrast to animals, most plants make their own food, through the extraordinary process of photosynthesis, using energy captured from the sun; most fungi break down decaying organic material (without ingesting it) into its chemical constituents and absorb released nutrients. Animal cells lack a rigid cell wall (some form of which is typical of plants and most fungi) and their cell biology and physiology differ in a variety of ways from other organisms.
The diversity of animals is impressive. Zhang (2011) recently coordinated an effort to outline a classification scheme for all known animals and to estimate species richness (i.e., number of species) in different parts of the animal tree. Results from this publication are enlightening. More than 1.5 million animal species have been described (and many more continue to be discovered and formally described each year). The phylum Arthropoda (insects, spiders, crustaceans, etc.) accounts for around 80% of this total; around 2/3 of the total is accounted for by the insects alone. Well over a third of all known insects (and around a quarter of all known animal species!) are beetles: nearly 400,000 different species of beetles have already been described. Among the known species of insects are also nearly 120,000 Hymenoptera (ants, bees, and wasps) and nearly 160,000 Lepidoptera (moths and butterflies). More than 40,000 spider species and over 50,000 species of Acari (mites and ticks) have been described. Nearly 70,000 species of Crustacea (crabs, shrimps, barnacles, pillbugs, and many groups completely unfamiliar to those who don't study them!) are known. The Myriapoda (millipedes, centipedes, and relatives) includes around 12,000 described species. The Mollusca (clams, snails, octopuses, and relatives) is among the largest of the animal phyla, with nearly 120,000 known species. There are over 17,000 known species of Annelida (segmented worms, including earthworms, "polychaete" worms, leeches, and their relatives), Even some groups most people have never even heard of are quite diverse. For example, there are over 1000 described Acanthocephala, over 3000 freely available online.