Short answers, pulled from the story.
A nymph in biology is the juvenile form of certain invertebrates, particularly insects that undergo gradual metamorphosis (hemimetabolism). Unlike a larva, a nymph already resembles the adult in body shape, lacking only wings (in winged species) and genitalia. Nymphs moult through multiple growth stages called instars and never enter a pupal stage before becoming adults.
Many insect orders have nymph stages, including Orthoptera (crickets, grasshoppers, locusts), Hemiptera (cicadas, aphids, shield bugs, leafhoppers), mayflies, termites, cockroaches, mantises, stoneflies, and Odonata (dragonflies and damselflies). Arachnids such as spiders, mites, and ticks also produce nymphs.
A naiad is a nymph of an aquatic insect, specifically juveniles in the orders Odonata, Ephemeroptera (mayflies), and Plecoptera (stoneflies). The word naiad comes from Ancient Greek mythology, where it named water spirits. In older literature, these aquatic species were sometimes called heterometabolous insects because their immature and adult stages live in different environments.
In 1628, English physician William Harvey published An Anatomical Disquisition on the Motion of the Heart and Blood in Animals, in which he hypothesized that the pupal stage in insects resulted from imperfect eggs. He argued that some eggs produced nymphs (small versions of mature insects) while others produced incomplete intermediate forms that required a second egg stage - the pupa - to reach adulthood. This "Second Egg Hypothesis" is now considered outdated.
Nymph fly patterns in fly fishing imitate the aquatic juvenile stage of insects such as dragonflies, mayflies, and stoneflies. In the United States, nymph patterns account for more than half of all fishing fly patterns regularly used for trout.
The biological term nymph comes from the Ancient Greek word nūmphē, meaning "bride." It was applied to the juvenile stage of hemimetabolous insects because the nymph already resembles the adult form, much as a bride is poised at the threshold between two life stages.