W supermarkecie jest dziś promocja na nabiał i świeże owoce.

Because after w meaning in / at a place, Polish normally uses the locative case.

• supermarket = dictionary form
• w supermarkecie = in the supermarket

So the ending changes:

• supermarket → supermarkecie

This is very common:

• w domu = in the house
• w sklepie = in the shop
• w supermarkecie = in the supermarket

Jest is the 3rd person singular form of być (to be) and here it means something like there is.

So:

• W supermarkecie jest dziś promocja... = There is a promotion in the supermarket today...

This is an existential structure: it says that something exists or is taking place somewhere.

It is not saying the supermarket is... It is saying a promotion is there.

Because the main thing being talked about is promocja (promotion/sale), and promocja is singular.

The structure is:

• jest promocja = there is a promotion
• na nabiał i świeże owoce = on dairy and fresh fruit

So the subject is not nabiał i świeże owoce. Those are just the products included in the promotion.

Promocja na is a very common Polish pattern meaning:

• a promotion on
• a sale on
• a special offer on

So:

• promocja na kawę = a promotion on coffee
• promocja na ubrania = a sale on clothes
• promocja na nabiał i świeże owoce = a promotion on dairy and fresh fruit

After na in this meaning, Polish uses the accusative case.

It is the accusative case, because promocja na takes the accusative.

So:

• nabiał stays nabiał
• świeże owoce is accusative plural

For inanimate plural nouns like owoce, the accusative is often the same as the nominative, so it looks unchanged.

That is why:

• owoce = fruits
• świeże owoce = fresh fruits
• after na, it still appears as świeże owoce

Nabiał means dairy products as a category: milk, cheese, yogurt, etc.

Grammatically, it is a singular masculine inanimate noun, even though in English we often think of it as a plural idea.

So Polish treats it like a mass/category noun:

• ten nabiał = this dairy produce
• lubię nabiał = I like dairy products

That is why you see:

• na nabiał not na nabiały

Because the adjective must agree with the noun in number, gender, and case.

Here:

• owoce = plural
• it is a non-masculine-personal plural noun
• so the adjective takes the ending -e

That gives:

• świeże owoce = fresh fruit / fresh fruits

Compare:

• świeży chleb = fresh bread
• świeża kawa = fresh coffee
• świeże owoce = fresh fruit

Polish very often uses owoce (fruits) where English may prefer fruit as a mass noun.

So both ideas are normal, but Polish commonly says:

• świeże owoce = fresh fruit / fresh fruits

English translation may use either, depending on style.

Dziś means today.

It tells you when the promotion is happening:

• W supermarkecie jest dziś promocja... = There is a promotion in the supermarket today...

Polish word order is fairly flexible, so dziś could appear in other places too, for example:

• Dziś w supermarkecie jest promocja...
• W supermarkecie dziś jest promocja...

All are understandable, though they may sound slightly different in emphasis.

They both mean today.

• dziś is a bit shorter and often feels slightly more compact
• dzisiaj is also very common and completely natural

In this sentence, you could say:

• W supermarkecie jest dziś promocja...
• W supermarkecie jest dzisiaj promocja...

Both are correct.

Yes. Polish word order is more flexible than English because cases show the grammatical relationships.

The original sentence is natural because it starts with the location:

• W supermarkecie jest dziś promocja na nabiał i świeże owoce.

But you could also say:

• Dziś w supermarkecie jest promocja na nabiał i świeże owoce.
• Promocja na nabiał i świeże owoce jest dziś w supermarkecie.

These all mean roughly the same thing, but the emphasis changes:

• starting with W supermarkecie highlights the place
• starting with Dziś highlights the time
• starting with Promocja highlights the promotion itself

Because Polish has no articles like a or the.

So:

• supermarket can mean a supermarket or the supermarket
• promocja can mean a promotion or the promotion

You understand which one is meant from context.

So w supermarkecie literally just means in supermarket, but in natural English we translate it as in the supermarket.

It is a loanword used in Polish, borrowed from English, but it behaves like a normal Polish noun and gets Polish endings.

For example:

• supermarket = supermarket
• supermarketu = of the supermarket
• supermarkecie = in the supermarket

So even borrowed words are usually declined in Polish.

A natural neutral reading would usually stress the important information near the end, especially the products on sale:

W supermarkecie jest dziś promocja na nabiał i świeże owoce.

If you want to emphasize a different part, you can do that with intonation:

• stress dziś if the key point is today
• stress w supermarkecie if the place matters
• stress nabiał i świeże owoce if the products are the focus

That flexibility is one reason Polish word order can move around more than English.