Independence:The virtue of self-reliance.
A common usage of this term upholds financial self-reliance. It says you should be able to live off of your own money and efforts, instead of having to rely on other people. The advantage of this is that it leaves you fully in control of your life, allowing you to make your own decisions and live the way you think is proper. Without the financial self-reliance, you would have to ask permission to make choices in your life.
Objectivism goes beyond financial self-reliance and upholds mental self-reliance as well. It says you should learn to make your own value judgments, identify facts, learn about the world, etc. You shouldn't rely on others to tell you what to value, or what to think. You should use your own best judgment, and rely on yourself. You should directly deal with reality, instead of having others act as middlemen.
This is the general principle. Interact directly with reality. When others act as your middleman, you lose your ability to make choices and pursue your own values. You become unnecessarily reliant on them, which negatively hurts your own life. If you make it your business to be self-reliant, it creates new opportunities. When you're the one who understands reality, you can figure out what you don't know and go and learn it. When you are financially self-reliant, you can understand how you might increase your wealth or ability to produce wealth.