Being independent refers to the act of being in charge of yourself, and the consequences of your actions, instead of being subservient to other people, or other forces. Below are some basic understandings
When you are directly in charge of yourself, you will have an understanding of how your own personal actions and thoughts affect reality. You are not subservient to anybody else and can see clearly what affects your actions are having in the environment around you. This increase your discipline of the body and mind, in which you continue to make the right decisions towards your goal.
You are not living someone else's passion, but your own. When you live your own passion, you can connect to within your passion and increase its energy even more. This correlates in an increase in mental and physical manifestation directly. You will get more ideas about your goal, and you will develop a clear plan of how to apply your ideas to achieve material manifestation.
If somebody else is doing all the work for you, you can't understand the main principles and variables which are creating the success. When you take charge of the ropes yourself, you can see exactly what works and what doesn't.