You might think of an atom as being like a tiny solar system, with protons and neutrons in the center and electrons orbiting around them like little planets. This model is good enough for describing what an atom is, but it turned out to be not good enough for describing what an atom does.
The quantum model changes the electron from an orbiting particle, to what amounts to being a wave of energy-with-mass occupying the area that could be called the electron's orbit. (If it helps, a photon is like this too: a wave of energy that acts like a particle.) Using that assumption, it tells scientists why an electron can only carry, absorb or release exact amounts of energy according to the wavelength of the orbit it lives in. Such behavior explains things like the color of light emitted by an excited atom or how a photocell turns sunlight into electricity.