What Does "Still Waters Run Deep Mean"?

This is an old proverb or saying. It means that people who are very quiet, especially people who don't talk about or draw attention to themselves, will often surprise you. They may turn out to have something unexpected in their past, or to have done things you wouldn't expect. More often though, it refers to their character: eg, the person has very strong feelings which they don't reveal.

An example sentence might be: "I know she didn't seem upset when she split up with her boyfriend, but really she was heartbroken; still waters run deep."

The saying is based on the literal fact that it is often shallow streams and rivers which move more swiftly and look more "alive" whereas deeper water may have little activity on the surface.