Matte-finish refers to the sheen of a material. Sheen is the extent to which the surface of a material reflect light. Matte is a non-standardised term that refers to a low level surface sheen. Light that hits a matte surface will be diffused at a range of angles, the opposite of a mirror finish.
A matte finish can be affected by a number of things, including the ratio of pigment to material volume and the material's refraction index.