The wave-particle duality is that some electromagnetic radiation phenomena appear more like particle interactions than wave interactions despite the fact that electromagnetism has long been confirmed as wave-like, and conversely, some particle phenomena at an atomic scale are wave-like.
Albert Einstein pointed out some observed characteristics of the photoelectric effect could be explained if EMR acts like particles whose energy is related to the wave's frequency. (Photon is our term for such a particle of EMR.) Louis de Broglie later explored the converse as a hypothesis, i.e., that particles have a similar wave-like aspect (matter waves, with the de Broglie wavelength), and uncovered in it a means to carry out quantum-mechanical calculations for the behavior of particles. Wave-like behavior was subsequently confirmed in particle experiments, e.g., producing situations where the behavior of electrons appeared like waves rather than particles.