Someone who is ‘independent’ is not reliant upon or associated with another person or organization. They do not need help or money from anybody else. ‘An independent voice’ is a person speaking from a place of independence, who is not receiving support or funding associated with any of the things they are talking about. They, therefore, are in a position which affords them impartiality and the ability to be unbiased. A journalist or judge is a good example of an ‘independent voice’ on a matter. This is a formal phrase you are more likely to hear in professional environments.