Topological order is a new kind of order in quantum matter, which corresponds to pattern of long-range quantum entanglement. See http://en.wikipedia.org/wiki/Topological_order
Topological order is a new kind of order in zero-temperature phase of matter (for example, quantum spins, bonsons, and/or electrons). The new order corresponds to pattern of long-range quantum entanglement. Topological order is beyond the Landau symmetry-breaking description. It cannot be described by local order parameters and long range correlations. However, topological orders can be described/defined by a new set of quantum numbers, such as ground state degeneracy, non-Abelian geometric phases of degenerate ground states, quasiparticle fractional statistics, edge states, topological entanglement entropy, etc. Fractional quantum Hall states and quantum string liquids are examples of topologically ordered phases.