A nymph imitates the immature, underwater stage of an aquatic insect. Most of a trout's diet — by some estimates 80%+ — is sub-surface, so a fly that drifts or sinks through the water column matches what they're actually eating most of the day.
"Nymphing" is shorthand for the technique: dead-drift the fly along the bottom, often under a strike indicator, watching for the indicator to twitch.