Independent financial advice is the type of advice you would expect to receive from an investment professional that is not also in the business of selling products or services other than the advice.
The great majority of people who offer financial advice do so in conjunction with the ability to sell you the products and/or services associated with the advice being offered. For example, if the advice is to reallocate your portfolio or to buy or sell a particular investment, the person offering the advice may have a vested interest in making the recommendation in that they can make money on the transaction and /or the value of your portfolio. That is the case with brokers and investment advisors. This is not to say that the advice is bad or improper; you just need to be aware that there may be other possible motivations behind the advice.
The person you are most likely to receive independent financial advice from is an investment professional that does not have a financial interest in whether or not you take the advice. This is the case with fee-only financial planners. They charge a fee only for the giving of advice, not in the execution of the advice.