Ne t’en fais pas !

Let’s put this imperative phrase in the declarative negative form.

Tu ne t’en fais pas. [You don’t worry (about it). You are not worried.]

We have the prenominal verb se faire conjugated.

See here for its various meanings:
http://www.larousse.fr/dictionnaires/francais/se_faire/32706

En has the grammatical function of a pronoun. It replaces de. In English we often neglect “about it”, in (correct) French is not so omitted.

E.g.

Il ne se fait pas de sa santé.

If we don’t want to repeat de sa santé, one may say

Il ne s’en fait pas.

As further examples:

Elle s’en souvient (se souvenir de). She remembered it.

Elle lui en fut reconnaissante. She was grateful to her for it.

J’en ai trouvé huit. I found eight (of them).

This is a wholly idiomatic expression, meaning the structure is not really analyzable.

In his answer, dimitris made a good effort in analyzing en as a pronoun replacing de + noun phrase. That is indeed how en normally works.

But this is not correct, so let’s take the opportunity to learn a relevant principle:

• Some verbs can take an optional complement using a preposition. In that case, the dictionary entry gives the basic meaning of the verb, and when you add a complement, the basic meaning doesn’t change.

  • For example, parler means “talk”. And if you parler de something, you “talk about” it.

• Other verbs have a non-optional complement built in. In that case, you’ll find separate dictionary entries with and without the complement and they’ll often have different meanings.

If we look at the Larousse entry for se faire that dimitris cited, we see that none of the entries are “worry”. That tells us that adding de to this entry will not yield “worry about something” because that would be a significant change in meaning.

Instead, we have to find an entry that looks like se faire de or s’en faire — where the complement is built into the entry, not optional.

Unfortunately, Larousse’s online version is pretty weak for expressions. But WordReference, though not the most authoritative dictionary, is good for them. Here’s the entry for s’en faire:

s’en faire loc v (s’inquiéter) • worry • fret

Here we have the meaning we’re looking for, so we know we’ve found an idiom and can’t remove or analyze en. The use of locution verbale is also a hint that this is a fixed expression.

This also means that we don’t need en to refer to anything in particular, and it even means that we can use an entirely different preposition to add a complement, as in Stéphane’s example:

Il ne s’en fait pas pour sa santé.

Another example of verb like this is n’y voir rien, meaning “not be able to see”. Even though y is normally a pronoun replacing a location, in that expression it has no analyzable meaning.

I’m French, so sorry if my English isn’t perfect but I thought I could help.

In French, we have a lot a expressions to say to be worried.

Se faire de la bile.

Se faire du soucis.

Se faire du mauvais sang.

And there are also the negative forms :

Ne pas se faire de bile.

Ne pas se faire de soucis.

Ne pas se faire de mauvais sang.

If you consider these, you can say that ne pas s’en faire is a contracted form of them where s’en refers to bile/soucis/mauvais sang.