Mayflies:

On many trout streams across the world, the mayfly is the most abundant food source for trout. Mayflies are typically available to the fish all year in either their nymphal form or as a winged adult often, both are present. The mayfly is most probably the most important aquatic insect to the trout fly fisherman.

Mayflies are any of an order (Ephemeroptera) of insects with an aquatic nymph and a short-lived, fragile adult lacking mouthparts and having membranous, heavily veined wings and two or three long, threadlike tails. NOTE: the wings of the mayfly are held vertically above the body when closed. 

Over 3,000 species of mayfly are known worldwide, grouped into over 400 genera in 42 families. The mayfly has three separate stages in its life. They are NymphSubimago and Imago. In all three stages mayflies are available to fish. In fly fisherman "talk", the subimago is known as a dun and the imago is known as a spinner.

Nymphs are Immature mayflies. There are four basic kinds of mayfly nymphs. They are swimmers, clingers, crawlers and burrowers. These terms refer to how they live in the underwater environment. If you want more information here are some links to good information: