long-range order
Long-range order is what makes a crystal a crystal. Picture standing in a vast, perfectly planted orchard: once you know the spacing of the first few trees, you can predict exactly where a tree sits a mile away. Long-range order means the atomic arrangement is predictable over huge distances, knowing the local pattern lets you locate atoms billions of spacings away with certainty.
Formally, long-range order is periodicity: the structure is unchanged under repeated translation by the lattice vectors, so the pattern at one point recurs identically at every equivalent point across the whole crystal. This is the defining property of the crystalline state. It is what produces sharp diffraction peaks, the periodic repeat acts like a diffraction grating, and only a truly repeating array gives crisp, well-defined spots. A quasicrystal is the subtle exception: it has long-range order (sharp spots) without ordinary periodicity.
Long-range order is the dividing line in the great structural divide. Materials that have it (crystals) get flat faces, sharp melting points, and diffraction spots; materials that lack it (glasses, liquids) do not. Caveat: order and disorder are not all-or-nothing, a solid can have perfect long-range order in where its atoms sit yet disorder in which kind of atom occupies each site (as in a disordered alloy), so one must always ask, order of what?
Stand in a perfectly planted orchard and measure the spacing of the first few trees, and you can work out where a tree sits a mile away. A crystal's long-range order is exactly this predictability across vast distances.
Long-range order: local spacing predicts every distant atom's position.
Long-range order refers to a repeating pattern, not to whether every site is identical. An alloy can be perfectly periodic in position yet randomly mixed in chemistry, positional long-range order with chemical disorder.