This idiom or expression is about:

Supporting, believing in someone or something.
Defending or protecting someone, their ideas, their honor, their physical well-being, etc.

I’m tired of being a quiet observer. Starting today, I’m standing up for victims of violence and their rights!

Also see:
Taking a stand.

This idiom or expression means:

Choosing a cause.
Supporting someone or something.

When someone says: It’s time for you to take a stand, they mean something like:

You can’t remain indifferent any more.

Also see:
Standing up for.