In Part 2 of her lesson on negation, Patricia explains three common negative constructions: rien ne... (nothing), ne... aucun(e) (not any), and ne... nulle part (nowhere). In a few of her examples, she uses the pronoun en, which some beginners might not be familiar with: 

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Veux-tu quelques pommes? Non, je n'en veux aucune.

Do you want some apples? No, I don't want any.

Captions 41-42, Le saviez-vous? - Les différentes négations - Part 2

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As-tu quelques stylos à me passer? -Non, je n'ai aucun stylo. Je n'en ai aucun.

Do you have some pens to give me? -No, I don't have any pens. I don't have any.

Captions 53, 57-58, Le saviez-vous? - Les différentes négations - Part 2

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In English, we know that the "any" of "I don't want any" and "I don't have any" refers back to "apples" and "pens," respectively. But in French, we can't just say je ne veux aucune and je n'ai aucun. We need to add en to refer back to the objects in question—quelques pommes and quelques stylos.

To make this clearer, let's simplify these sentences by making them affirmative:

Veux-tu quelques pommes? -Oui, j'en veux.
Do you want some apples? -Yes, I want some.

As-tu quelques stylos à me passer? -Oui, j'en ai.
Do you have some pens to give me? -Yes, I have some.

Just as it would be incorrect to respond to the English questions with "yes, I want" and "yes, I have," in French you wouldn't say oui, je veux or oui, j'ai. You need to specify what you're referring to. So you add "some"/en. As you can see, while "some" is placed right after the verb, en is placed right before.

Though the examples above use quelques (some), the general rule for en is that it replaces de + a noun. In fact, we can rewrite these sentences using des instead of quelques without changing their meaning: 

Veux-tu des pommes? -Non, je n'en veux aucune. 
Do you want some apples? -No, I don't want any.

As-tu des stylos à me passer? -Non, je n'en ai aucun.
Do you have some pens to give me? -No, I don't have any.

There's also an example of en replacing de + a noun later on in the video:

Y a-t-il de la neige partout? Non, il n'y en a nulle part.

Is there snow everywhere? No, there's not any anywhere.

Captions 71-72, Le saviez-vous? - Les différentes négations - Part 2

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If you want to avoid using en for now, you can simply include the object you're referring to in the sentence:

Y a-t-il de la neige partout? -Non, il n'y a pas de neige nulle part.
Is there snow everywhere? -No, there's no snow anywhere.

Veux-tu quelques/des pommes? -Non, je ne veux pas de pomme.
Do you want some apples? -No, I don't want any apples.

As-tu quelques/des stylos à me passer? -Non, je n'ai aucun stylo [or: je n'ai pas de stylo].
Do you have some pens to give me? -No, I don't have any pens.

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For an in-depth look at negation in French, be sure to check out the rest of Patricia's videos on the subject.