Wave-particle duality is the concept that matter and energy have both a wave nature and a particle nature. It is a fundamental result predicted by quantum mechanics.
Whether waves or particles are better suited for describing a system depends on the circumstances. For example, light is usually characterized as waves in most every-day applications, but photons (light particles) must be considered in some situations, such as the photoelectric effect and most particle physics experiments.
The wave characterization may be nothing more than than a manifestation of the underlying positional uncertainty of a particle, which disappears upon observation.