Independently means doing something on your own, without help or control from others. When you solve a math problem independently, you figure it out yourself instead of copying from a friend or asking for hints. When two scientists working in different countries independently discover the same thing, they each made the discovery without knowing about the other's work.

The word suggests real capability and self-reliance. A student who can read independently doesn't need someone sitting beside them sounding out words. A country that becomes independent governs itself rather than being ruled by another nation. The American colonies fought to become independent from Britain, meaning they wanted to make their own decisions and control their own future.

Independence (the noun form) is the state of being independent. People value independence because it shows they've developed the skills and judgment to handle things themselves. When your parents let you walk to school independently, they trust that you know the route and can stay safe. When you complete a project independently, you prove you can organize your time, solve problems, and finish what you start without constant supervision.