In computing, processing information simply means performing a task. It means transforming data from one form to another.
In the real sense of it, it means, performing arithmetic or logical operations (by ALU) on binary data which could result in transmitting data from input devices to output devices. When a user launches the calculator application on his PC, and he tries to do some arithmetic (which is processed by the ALU) by entering numbers using his keyboard/mouse (input devices), he gets the result on the screen(output device). This scenario is a typical example of processing information.