They sell (some) books.

is

Elles vendent des livres.

Whereas some can be omitted in English, in French the indefinite article (un/une/des) cannot do so.

When there is an adjective that follows the noun, the rule is the same, that is:

Elles vendent des livres intéressants.

However, with adjectives that precede the noun and in careful French, des becomes de, so that:

Elles vendent de vieux/nouveaux livres.

It is not so uncommon to encounter des+adjectif+noun in everyday speech (de does not sound the same as des).

Note also the difference:

Je vois de petits enfants qui jouent.

and

Je vois des petits-enfants qui jouent. (grandchildren)

The difference is based upon the composed (fixed) form adjective+noun.

Other examples include:

• des grands-pères ; des petits pois ; des beaux-parents, etc.

En as personal pronoun replaces the form:

Elles vendent des livres.

Elles en vendent.

In fact, des livres is COD (complément d’objet direct) of the verb vendent.

It can also replace the form:

Elles vendent de vieux livres. Elles en vendent.

The so-called complément d’adjectif can be replaced in certain cases as in the example below:

Elles vendent de vieux livres. Elles en sont fières. (i.e. être fier de vieux livres)

Suggested reading:

https://www.francaisfacile.com/exercices/exercice-francais-2/exercice-francais-4045.php

http://bdl.oqlf.gouv.qc.ca/bdl/gabarit_bdl.asp?id=3496

http://bdl.oqlf.gouv.qc.ca/bdl/gabarit_bdl.asp?t1=1&id=3513

We need the “de” because in French it’s incorrect to use “vendre” without using an article (le/la/les/un/une/de/des).
You have to use something after “vendre”.

BUT the word can be tricky to choose..

Are you speaking about something in general, not specifically? You have to use un/une/des if you can count it, or de/des if you cannot.

• “Je vends des voitures” = “I sell cars but it doesn’t matter which ones and i can count how many cars i sell”
• “Je vends de la farine” = “I sell flour” (you can’t count flour)

In your exemple “Elles vendent de vieux livres.”, de is used instead of des because in French, “des” becomes “de” when placed before an adjectif.

You speak about that precise item ? You have to use le/la/les

• “Je vends la voiture” = “I sell this specific car whom we are talking about”

You want to tell where you are selling? Use en/à/dans if you want to tell precisely where, or en if you are inexplicit
“Je vends des voitures en France” = “I sell cars in France”
“Je vends des voitures à Paris” = “I sell cars in PAris”

You are already talking about what you are selling ? Right, you can even use vendre without anything else after it.

• “Tu vends des voitures ?” “Oui j’en vends” (or “Oui je vends ceci”)
• “Do you sell cars?” “Yes I do” (or “Yes i sell this”)

TL;DR

Use “vendre de” when you sell something uncountable or when you remain vague (use “des” in this case or “de” before an adjective).
Replace it with a personnal pronoun or “les” when you sell something specific.