Meaning:

You use this proverb to say that a picture can give you as much information as a written or spoken text with a lot of words can.
If someone says, "A picture is worth a thousand words," he/she means that you can describe something by drawing just one picture as well as you can by writing or saying a lot of words.

People also say "A picture paints a thousand words."

Example:

Thank you for trying to give me directions, but it's too confusing to me. Would you mind drawing a map for me? A picture is worth a thousand words.

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