Here's an example illustrating divisional applications. 

Inventor John files a patent application June 1, 2013 claiming a new type of air conditioner unit and a new type of furnace. Both the air conditioner and the furnace use completely different principles to work, but since John isn't familiar with patent law, he puts them both in the same patent application (they are both household, temperature regulating appliances invented by him so he believes they can just be submitted together).

Months after filing the application, the PTO lets John know he filed incorrectly. He should not have included more than one invention in the same application out of convenience.

Let's go over John's options.

Basically, either the air conditioner or the furnace must go from the application. John immediately chooses to keep the furnace in the original application. But does he totally lose out on the air conditioner idea? Or can he file a brand new application for the air conditioner?

The best solution is for John to file a divisional application claiming the air conditioner. His original application could now claim the furnace only and the divisional could claim the air conditioner.  If done properly, both applications will have the same filing date, the date he filed the original application on, which was June 1, 2013.

One note to make is that divisional applications must be filed while the original application is still pending.