What is a productive cough?

We should be in the final throws of the pneumonia.  A cough,  not too loud or barky, has emerged in the past few days.  Doc said Miles would "cough it out"- and "it" I guess refers to the pneumonia, and the cough should be productive.  He seems a little sickly tonight- no fever, but pretty grumpy, and the reflux is kicking into high gear.  Bet the cough could be reflux relate- but I do hear some chest rumblings with some of the louder coughs.  How do I know that this is a productive cough or something else?  I am getting a little worried.