a close-packed plane
Look at one layer of a grocer's orange pyramid: each orange nestles into the hollows between six others, packed as tightly as circles can tile a flat surface. A close-packed plane in a crystal is a single sheet of atoms arranged in just this way — a two-dimensional hexagonal net where every atom has six in-plane neighbours and the discs cover the maximum possible fraction of the plane, about 91 percent.
The whole architecture of the densest metals is built by stacking these identical close-packed layers. Face-centred cubic stacks them in the order ABCABC, and its close-packed planes are the {111} family. Hexagonal close packing stacks them ABAB, and its close-packed plane is the basal plane (0001). Both stackings fill 74 percent of space and give each atom twelve neighbours, differing only in how the layers are offset. The close-packed plane is where slip most easily occurs and, in many crystals, the plane of cleavage.
Be careful with a common overstatement. Body-centred cubic has no truly close-packed plane at all; its densest plane, {110}, is well packed but not the perfect hexagonal layer, and BCC overall fills only 68 percent of space. So distinguish the densest plane in a given structure from a genuine close-packed layer — they are not always the same thing.
Face-centred cubic and hexagonal close packing are both built from identical close-packed layers, differing only in stacking: FCC is ABCABC (close-packed plane {111}), HCP is ABAB (close-packed plane (0001)). Both reach 74 percent packing and coordination number 12.
A close-packed plane is one hexagonal layer; how you stack such layers gives FCC or HCP.
Body-centred cubic has no true close-packed plane; its densest plane {110} is not a perfect hexagonal layer, and BCC fills only 68 percent of space versus 74 percent for FCC and HCP.