The word independent has several related meanings depending on the context. Here are the most common definitions:

As an adjective:
Not controlled by others:
"She is an independent woman who makes her own decisions."

Not connected or affiliated with a group or organization:
"He is an independent candidate running for office."

Self-sufficient or self-reliant:
"After moving out, he became financially independent."

Not influenced by others in opinion or behavior:
"An independent thinker who challenges conventional wisdom."

Separate from others; distinct:
"Two independent events in probability theory."

As a noun:
A person who is not a member of a political party:
"She votes as an independent in every election."

A small business or entity not owned by a larger corporation:
"The film was produced by an independent studio."