Miller indices are a notation system used in crystallography to describe the orientation of crystal planes and directions in a crystal lattice. They are represented by three integers (h, k, l) that correspond to the intercepts of the crystal plane with the axes of the crystal lattice. The values are derived by taking the reciprocal of the intercepts and then clearing any fractions to obtain the smallest whole numbers. These indices help scientists and engineers understand the geometric arrangement of atoms in a crystal, which is crucial for determining the material's properties. By using Miller indices, researchers can communicate effectively about different crystal structures and their characteristics in fields like materials science and solid-state physics.