Call back methods are ones that are "called back" after something happens. For example a client may order an ice cream and wait for it to be made. A call back method named say - onIceCream() will notify the client that the ice cream is now ready to be eaten. Some one will have to execute the onIceCream() method to tell the client that the ice cream is ready.
In EJBs for example the container will call back certain methods to notify the bean that something has happened. Example: ejbPassivate() is called before a bean is passivated. This is to let the bean know that it is about to be passivated and it should prepare itself for the same.