There are two possible modes of vibrations of atoms in the crystal:
In case of longitudinal mode the displacement of atoms from their equilibrium position coincides with the propagation direction of the wave, whereas for transverse mode, atoms move perpendicular to the propagation of the wave.
For one atom per unit cell the phonon dispersion curves are represented only by acoustical branches. However, if we have more than one atom in the unit cell optical branches will appear additionally. The difference between acoustical and optical branches arises because of the more options of vibrations for atoms in the unit cell. For example, atoms A and B of diatomic cell can move together in phase (acoustical branch) or out of phase (optical branch). Click here to see how it looks like
Generally, for N atoms per unit cell there will be 3 acoustical branches (1 longitudinal and 2 transverse) and 3N-3 optical branches (N-1 longitudinal and 2N-2 transverse)