Why the name "optical phonon"? Why do we have two different types of phonons, optical and acoustical? Why are they called optical phonons? 
 A: As I understand this occurs when a cystalline solid has more than one atom in the primitive cell of the lattice. For simplicity I'll consider the case of two types of atoms, distinguished by their position in the primitive cell (but which may or may not be otherwise identical).  This gives rise to multiple modes of vibration.  The acoustical phonon corresponds to both types of atoms moving in phase in the long wavelength limit (that is, near the center of the 1st Brillouin zone), whereas the optical phonon corresponds to the two types moving out of phase, such that adjacent atoms move in opposite directions in the long-wavelength limit.
(For the case of only one atom in the primitive cell, you can also get adjacent atoms moving in opposite directions, but this happens at the edge of the 1st Brillouin zone, in the limit where the wave becomes a standing wave.)
They are called "optical" because in ionic crystals they can be excited by EM radiation, with the positive ions moving one way while their negatively charged neighbors move the other way.
We can see the two modes from the dispersion relation, which for two atoms in the primitive cell (in the 1-dimensional case) is given by:
$$\omega^2 = \beta \left( \frac{1}{m} + \frac{1}{M} \right) \pm \sqrt{\left( \frac{1}{m} + \frac{1}{M} \right)^2 - \frac{4 \sin^2 ka}{Mm}}$$
Here m and M are the masses of the two types of atoms.  There are two branches, the lower of which is the acoustical branch and the higher of which is the optical branch, with a gap between them.  (Note that the two branches still exist for equal masses, but the gap closes.)
Equation copied from this site, which also has this nice animation of the two modes.
