a family of planes
Just as directions come in symmetry-equivalent bunches, so do planes. A family of planes gathers every plane that the crystal's symmetry can map onto a given one, and we write it in curly braces, {hkl}. The six faces of a cube are the plainest example: they look different only because of how you are holding the cube, but to the crystal they are the same kind of surface. That whole set is written {100}.
In a cubic crystal the family {100} contains the three cube-face orientations (100), (010), (001) and their opposites — six faces in all. The family {111} contains the four octahedral planes (eight counting opposite faces), the ones you see as the flat triangular facets on a natural crystal of fluorite or diamond. As with directions, you build the members by permuting and sign-flipping the indices in every way the symmetry permits, and the count is fixed by the crystal system, not by a universal rule.
Families matter because equivalent planes behave identically. Cleavage — the tendency of a crystal to split along particular flat surfaces — happens along a whole family at once, which is why a cleaved rock-salt crystal always breaks into little cubes bounded by {100} faces. Naming the family, rather than one plane, captures that the same physics is available in several orientations.
Rock salt (NaCl) cleaves on {100}, so a struck crystal shatters into tiny cubes; fluorite (CaF2) cleaves on {111}, so it breaks into octahedra. Same idea, different family — the split follows whichever family of planes is weakest.
Curly braces name all symmetry-equivalent planes; cleavage and facets follow a whole family.
Do not assume {hkl} always has the cubic number of members. In lower-symmetry crystals the same braces gather fewer planes, because fewer symmetry operations relate them.