formula units per cell (Z)
Z answers a homely question: how many 'recipes' of the chemical formula fit inside one unit cell? If the formula is NaCl and Z = 4, then one cell holds four sodium atoms and four chlorine atoms — four helpings of the recipe. It is always a small whole number, and it ties the geometry of the cell to the chemistry of the material.
You find Z by counting the cell contents through the Wyckoff multiplicities. In rock salt, sodium fills the 4a site (multiplicity 4) and chlorine the 4b site (multiplicity 4), giving 4 Na and 4 Cl — that is 4 NaCl units, so Z = 4. Z then feeds straight into the density formula: rho = Z times M / (N_A times V_cell), where M is the formula mass, N_A is Avogadro's number and V_cell the cell volume. For NaCl with a cube edge a = 5.64 angstrom (V = a^3 = 1.79 times 10^-22 cm^3) and M = 58.44 g/mol, rho = 4 times 58.44 / (6.022 times 10^23 times 1.79 times 10^-22) = about 2.16 g/cm^3 — bang on the measured value.
Z is not a free choice; it is fixed by how the formula partitions across the Wyckoff sites the atoms occupy, which in turn is set by the space group. Every published crystal structure quotes Z, because it is the checksum that makes the numbers hang together: cell volume (geometry), composition (chemistry) and density (mass) must all agree. If your calculated density is off by a factor of two, a wrong Z is the usual culprit.
Copper is face-centred cubic with atoms at the 4a-type site, so Z = 4 atoms per cell. With a = 3.61 angstrom and M = 63.55 g/mol the density works out to about 8.96 g/cm^3 — exactly what a scale measures for copper metal.
Z links a cell's geometry to its mass and lets you predict density from structure alone.
Z counts formula units, not atoms. For NaCl (Z = 4) there are 8 atoms in the cell; for a protein with one molecule of formula per asymmetric unit and four asymmetric units, Z = 4 may mean thousands of atoms. Always check which the source means.