What is Lattice plane, Miller indices, interplanar spacing?

A lattice plane is a plane through at least three non-aligned nodes; it belongs to a family of parallel, equally spaced planes that contain every node. If the plane of the family nearest the origin cuts the axes at $a/h$, $b/k$, $c/l$, the integers $(hkl)$, without common factor, are its Miller indices (an index 0 for a plane parallel to an axis). The distance between adjacent planes is the interplanar spacing $d_{hkl}$.