a primitive cell
A primitive cell is the smallest possible unit cell — the most economical stamp, containing exactly one lattice point. It is the leanest chunk that still tiles all of space; you cannot make a valid repeating cell any smaller.
Exactly one lattice point is the definition. A primitive cell has lattice points only at its corners; since in 3D each corner point is shared among 8 neighbouring cells, 8 corners times 1/8 = exactly 1 point. Its volume equals the volume of space per lattice point. For example, the FCC conventional cubic cell holds 4 lattice points, so its primitive cell has 1/4 the volume — a smaller rhombohedron spanned by vectors pointing to the face-centre neighbours.
Smallest is not always the most convenient. The primitive cell of FCC is a squashed rhombohedron with 60-degree angles that hides the cubic symmetry, so crystallographers usually prefer the larger, obviously-cubic conventional cell. Smallest and most-symmetric are different goals; you pick according to purpose.
The FCC conventional cube has 4 lattice points, so its primitive cell has 1/4 the volume and contains exactly 1 point. That primitive cell is a rhombohedron with edges (a/2)[110], (a/2)[101], (a/2)[011] and 60-degree angles — smaller, but it no longer looks cubic.
The primitive cell of FCC is a small 60-degree rhombohedron with one lattice point.
Every lattice has infinitely many valid primitive cells (all of equal volume, one point each); the Wigner-Seitz construction picks out the unique one that also displays the lattice's full symmetry.