Here are some important definitions:
A space lattice provides the framework with reference to which a crystal structure can be described. A lattice is different from crystal. In fact, a lattice gives rise to crystal when lattice points are replaced by atoms, ions, or molecules.
A 2-D or 3-D lattice is a regular arrangements of points. In order to specify it completely, only a small part of the lattice is described. This figure is known as a unit cell.
In 2-D, there are 5 possible lattices namely, square, rectangle, hexagonal, parallelogram and rhombic.
In 3-D, there are 14 possible lattices, and these lattices are called Bravais lattices (after the French mathematician who first described them) like cubic primitive, hexagonal primitve, etc.
In a cubic system there are 3 possible Bravais lattices possible namely, primitive, body centered and face centered.
Similarly in hexagonal crystal system there is only one Bravais lattice viz, Primitive.
Crystallographers have been able to divide 32 point groups and 14 space lattices into seven crystal systems and 14 Bravais lattices. Remember that the primitive cells of any two crystals are not the same. Primitive unit cells mean that the lattice point must be at the corners of the unit cell.
HCP is ABA-ABA arrangement of layers in which tetrahedral void of second layer are covered by the third layer.