When you are comparing two things, the first one is known as the former and the second as the latter. For example, George Bush and George W. Bush were both U. S. presidents. The latter was the son of the former.
The word latter is really a form of later meaning "more recent" or "that which came after." The latter recording of a band refers to the one made more recently. It also can refer to a later time, near the end. If someone is in the latter stages of a disease, the disease has just about run its course and the person is about to die.