Learn Hardcore French: Il y a du fromage sur la table, j'en veux un peu. - There is some cheese on the table, I want a bit of it.

Literally, it’s built from il (dummy subject), y (there), a (has), but you should just learn it as a fixed expression meaning there is / there are.
It does not change form for singular or plural:
- Il y a du fromage. → There is some cheese.
- Il y a des pommes. → There are some apples.

It’s different from c’est / ce sont, which usually introduce or identify something (C’est du fromage. = That’s cheese.).

Why is it du fromage and not le fromage or un fromage?

Because French normally needs an article, and du here is the partitive article, meaning some (cheese) / an unspecified amount of cheese.

du fromage = some cheese / cheese in general (uncounted, mass noun)
le fromage = the cheese (a specific cheese, already known)
un fromage = a cheese (one cheese, usually meaning a whole cheese, like a round or block)

In the sentence, we just mean there is some cheese (in general) on the table, so du fromage is correct.

Is du always just de + le?

Grammatically, yes: du = de + le (of the / from the), but in practice du has two main uses:

Partitive article (some) – that’s the use here:
- du fromage = some cheese
- de la viande = some meat
- de l’eau = some water
- des biscuits = some biscuits
Preposition + article meaning of the / from the:
- le goût du fromage = the taste of the cheese
- je viens du cinéma = I’m coming from the cinema

In Il y a du fromage, it’s the partitive article: we’re talking about an unspecified amount of cheese.

In English I can say “There is cheese on the table” without “some”. Why can’t French just say Il y a fromage?

Because in standard French, you almost always need an article before a noun.

English can often omit some:

There is (some) cheese on the table.

French cannot: the noun normally needs an article (definite, indefinite, or partitive):

Il y a du fromage sur la table. ✅
Il y a fromage sur la table. ❌ (ungrammatical in normal French)

So du is obligatory here to introduce fromage.

Why is it sur la table and not sur le table?

Because table is a feminine noun in French, so it takes the feminine article la, not le.

la table (feminine) → sur la table (on the table)
le lit (masculine) → sur le lit (on the bed)

You have to memorize the gender of nouns with them: une table, la table.

What exactly does en replace in j’en veux un peu?

En is a pronoun that replaces a phrase introduced by de, often meaning of it / of them or some (of it/them).

In this sentence:

Earlier we had du fromage (some cheese).
In j’en veux un peu, en stands for du fromage.

So j’en veux un peu literally means:
I want a little (of it) → I want a little (of the cheese).

This avoids repeating du fromage:

Il y a du fromage sur la table, j’en veux un peu.
= There is some cheese on the table; I want a bit of it.

Where does en go in the sentence? Can it move around?

In simple tenses, en goes before the conjugated verb:

J’en veux un peu. (I want some of it.)
Je n’en veux pas. (I don’t want any.)

With an infinitive, it goes before the infinitive it belongs to:

Je vais en manger un peu. (I’m going to eat a bit of it.)
Je ne veux pas en manger. (I don’t want to eat any.)

So the pattern is:
[subject] + (ne) + [pronouns, including en] + [verb] + (pas, etc.).

Why say j’en veux un peu instead of just je veux du fromage?

Both are correct, but they’re used slightly differently.

Je veux du fromage.
- Works fine as a standalone sentence.
- Introduces the idea of cheese; no previous mention needed.
J’en veux un peu.
- Normally refers back to something already mentioned with de or a partitive: here, du fromage.
- Sounds more natural as a response or continuation:
  - Il y a du fromage sur la table.
    — J’en veux un peu.

Using en avoids repetition and makes the link clear: of that cheese we just mentioned.

What’s the difference between un peu, un peu de, and peu de?

They all relate to quantity but with different nuances.

un peu = a little, a bit (without saying of what)
- J’en veux un peu. = I want a little (of it).
un peu de + noun = a little / a bit of (something)
- Je veux un peu de fromage. = I want a little bit of cheese.
- Il y a un peu de sucre. = There is a little sugar.
peu de + noun = little / not much (almost negative feeling)
- Il y a peu de fromage. = There is little cheese / not much cheese.
- Je bois peu de vin. = I drink little wine / not much wine.

In the original sentence, un peu is neutral: just a small quantity.

Could I say J’en voudrais un peu instead of J’en veux un peu? What’s the difference?

Yes, and it’s often more polite.

J’en veux un peu. = I want a little (of it).
- Direct, can sound a bit blunt in some contexts (though fine with friends).
J’en voudrais un peu. = I would like a little (of it).
- Uses the conditional voudrais, which softens the request and is more polite, especially when talking to strangers, in a shop, etc.

So if you’re asking someone to give you cheese, J’en voudrais un peu, s’il vous plaît is the very natural polite version.

Can fromage be plural (des fromages)? How would that change the meaning?

Yes, fromage can be plural:

du fromage (mass, uncounted) = some cheese (in general)
des fromages (countable, plural) = (several) cheeses / types of cheese

Examples:

Il y a du fromage sur la table.
There is some cheese on the table. (cheese in general)
Il y a des fromages sur la table.
There are cheeses on the table. (different cheeses or several individual cheeses)

Your original sentence focuses on cheese as a substance, not on counting separate cheeses, so du fromage is natural.

How would the sentence change if we talked about a clearly countable item, like apples?

You’d normally move from a mass noun (cheese) to countable plural (apples):

Il y a des pommes sur la table, j’en veux une.
There are apples on the table; I want one (of them).
Il y a des pommes sur la table, j’en veux quelques-unes.
There are apples on the table; I want a few (of them).

Notice:

des pommes = some apples (indefinite plural)
en still replaces des pommes: of them
The quantity word (une, quelques-unes, trois, etc.) goes after the verb:
- J’en veux trois. = I want three (of them).

How do you pronounce Il y a du fromage, j’en veux un peu?

Roughly in IPA:
[il‿j‿a dy fʁɔ.maʒ ʒɑ̃ vø œ̃ pø]

Breakdown with tips:

Il y a → sounds like eel-ya (often flowing together: [ilja] or [ija])
du fromage → dy froh-maj (final -e in fromage is mute, but the g is soft: ʒ)
j’en → zhahn (nasal vowel, like “zhahn”)
veux → vø (no pronounced x, lips rounded)
un peu → both have nasal/rounded vowels, roughly uh(n) puh

There’s no liaison between fromage and j’en; you pause slightly at the comma in normal speech:
Il y a du fromage sur la table, / j’en veux un peu.