the multiplicity factor
In a powder — millions of tiny crystals pointing every which way — many different planes end up diffracting to the same angle simply because they have the same spacing. The multiplicity factor counts how many symmetry-equivalent planes share a given d-spacing and therefore pile their intensities into one and the same powder peak. It is a pure counting number, and it can make one peak several times taller than another that has an identical structure factor.
The count comes from crystal symmetry. In a cubic crystal the six faces of the form {100} — namely (100), (010), (001) and their negatives — all have the same spacing a, so the {100} peak has multiplicity 6. The {110} form has twelve members (multiplicity 12), and {111} has eight (multiplicity 8). Lower-symmetry crystals split these into smaller groups, so the same nominal indices can have different multiplicities in, say, a tetragonal versus a cubic cell. The general planes {hkl} with all indices different and non-zero have the highest multiplicity of all.
This matters because a powder peak's measured intensity is the structure-factor intensity |F|^2 multiplied by the multiplicity (along with Lorentz-polarization and other factors). Forget the multiplicity and you will mis-estimate |F|^2 and get the atomic arrangement wrong. It is purely a powder-method effect: in single-crystal work each of the equivalent reflections is recorded separately, at its own place on the detector, so no such lumping-together occurs.
In a cubic powder pattern the (111) line collects eight equivalent planes (multiplicity 8) while (100) collects only six (multiplicity 6). Even if their structure factors were equal, the (111) peak would be about 8/6 = 1.33 times taller from multiplicity alone.
Multiplicity boosts peaks whose planes have many symmetry-equivalent twins; it is a counting factor, not a structural one.
Multiplicity is a powder-pattern effect only. In single-crystal diffraction the equivalent reflections land at separate spots and are measured individually, so no multiplicity factor is applied.