Constituents of matter, such as electrons can show wave-like nature in certain experiments, e.g. electron beams shone on a crystal with appropriate kinetic energy show a diffraction pattern not unlike X-ray diffraction patterns.
The hypothesis was one of the founding concepts in Quantum Mechanics because it established the wave-particle duality: the fact that matter can behave both as wave and as a particle. It seems counter-intuitive but has been proved to be true in many experiments, just like many other concepts in Quantum Mechanics. It helps explain a lot of natural phenomena, such as why an electron in orbit doesn’t lose its energy by radiation and fall into the nucleus and why do we have specific orbits (or energy levels, more accurately) around the nucleus.
“h” here is Planck’s constant and is equal to 6.62606957 x 10-34 J.s
“p” here is the momentum of the entity in question.