Compound eyes consist of many photoreceptor units or ommatidia. Each 'ommatidium' (singular) is an individual 'eye unit'.
The general picture
Eyes with resolving power have come in ten fundamentally different forms, and 96% of animal species possess a complex optical system. Image-resolving eyes are present in molluscs, chordates and arthropods.
Types of compound eye
Compound eyes fall into two groups: apposition eyes, which form multiple inverted images, and superposition eyes, which form a single erect image. Compound eyes are common in arthropods, and are also present in annelids and some bivalved molluscs.
Compound eyes, in arthropods at least, grow at their margins by the addition of new ommatidia.
Good fliers like flies or honey bees, or prey-catching insects like praying mantis or dragonflies, have specialized zones of ommatidia organized into a foveal area which gives acute vision. In the acute zone the eyes are flattened and the facets larger. The flattening allows more ommatidia to receive light from a spot and therefore higher resolution.
Another version is the pseudofaceted eye, as seen in Scutigera. This type of eye consists of a cluster of numerous ocelli on each side of the head, organized in a way that resembles a true compound eye.