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Essential: She left "because she had another meeting." (Here the phrase is needed to complete the meaning.)
Nonessential: I need to have two copies today, "because I am leaving tomorrow." (Here the meaning is complete without the phrase. The phrase is just extra info.)
I get the point, but if I were to teach this, I think my students would ask me why "she left" was not a complete sentence. The best answer I would be able to come up with, according to the logic shown here, would be that viewing the whole sentence the clause beginning with "because" is non-essential. But thanks for putting all those examples up on the web. Actually, I'm confused about the punctuation in my the first sentence in my comment. It seems that a lot of writers leave out the comma after "if were to teach this". But I'm not sure how to explain it?