It means that the Chest PA film is shot from the patient's back (posterior) through the chest to the front (anterior) of the chest. An AP chest x-ray is vice versa. The LAT chest x-ray is usually shot from the left side and also the right side. A cross table, or cross fire, chest x-ray is the same as a LAT chest.
Note: The answer above mine said "laterals from both sides." Usually just one lateral is done, a left lateral, that is with the left side closest to the image plate. Right laterals are usually not done, because the further away an object is from the image plate or film, the bigger and more distorted it will look...a right lateral places the heart further away and thus can make it look enlarged.