What is a Context Free Grammar?

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Can someone explain to me what a context free grammar is? After looking at the Wikipedia entry and then the Wikipedia entry on formal grammar, I am left utterly and totally befuddled. Would someone be so kind as to explain what these things are?

I am wondering this because I wish to investigate parsing, and also on the side, the limitation of a regex engine.

I'm not sure if these terms are directly programming related, or if they are related more to linguistics in general. If that is the case, I apologize, perhaps this could be moved if so?

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