Decaffeination

Decaffeination is a process which tries to remove most caffeine from things that contain it. Examples of plants that have caffeine in them are coffee beans, mate, tea leaves and cocoa. Soft drinks that do not have caffeine in them are sometimes called decaffeinated. While the caffeine is removed from some of them, it is simply not added to others, like Coca Cola. 
There are different processes to remove the caffeine.
Drinks that were produced from plants that had their caffeine removed are not free of caffeine; they still contain a little. It is simply not possible to remove all caffeine.