Kuchyňské potřeby jsou na stole.

Kuchyňské potřeby is a fairly broad phrase. It can mean things like:

• kitchen supplies
• kitchen utensils
• kitchenware
• kitchen necessities

So yes, kitchen utensils can be a good translation in many contexts, but potřeby is a little wider than just utensils.

• kuchyňské = kitchen
• potřeby = supplies / necessities / items

Together they refer to kitchen-related things in general.

Because the adjective has to agree with the noun it describes.

Here, potřeby is:

• plural
• grammatically feminine in the singular, but here used in the plural
• in the nominative case, because it is the subject of the sentence

So the adjective also takes the plural nominative form:

• kuchyňský = masculine singular
• kuchyňská = feminine singular
• kuchyňské = plural form used here

So:

• kuchyňské potřeby = kitchen supplies / kitchen utensils

Because potřeby is the plural form of potřeba in this meaning group.

In this sentence, it refers to multiple items, so Czech uses the plural:

• singular: potřeba
• plural: potřeby

Be careful, though: potřeba can also mean need, while potřeby often means supplies / items / necessities depending on context.

Jsou is the present tense, 3rd person plural form of the verb být = to be.

So:

• jsem = I am
• jsi = you are
• je = he/she/it is
• jsme = we are
• jste = you are
• jsou = they are

Since kuchyňské potřeby is plural, Czech uses jsou:

• Kuchyňské potřeby jsou... = The kitchen items are...

In this kind of sentence, Czech normally does use the verb být.

So:

• Kuchyňské potřeby jsou na stole. = The kitchen supplies are on the table.

Unlike Russian, for example, Czech does not normally omit to be in the present tense in standard sentences like this.

However, in informal labels, titles, notes, or very shortened speech, words may be omitted. But as a normal full sentence, jsou is correct and expected.

Because na can take different cases depending on meaning.

Here the meaning is location: the items are on the table, already there.
So Czech uses:

• na
  • locative for location

That gives:

• stůl = table
• na stole = on the table

If there were movement toward the table, Czech would use:

• na
  • accusative

For example:

• Dám to na stůl. = I’ll put it on the table.

So the contrast is:

• je to na stole = it is on the table
• dám to na stůl = I put it onto the table

Stole is the locative singular form of stůl.

The base form is:

• stůl = table

After the preposition na when it means location, Czech uses the locative:

• na stole = on the table

So:

• nominative: stůl
• locative: stole

Because Czech does not have articles like a or the.

So Czech simply says:

• Kuchyňské potřeby jsou na stole.

Depending on context, that can mean:

• The kitchen utensils are on the table.
• Kitchen utensils are on the table.
• The kitchen supplies are on the table.

English forces you to choose whether to use an article, but Czech usually leaves that to context.

The given word order is normal and neutral:

• Kuchyňské potřeby jsou na stole.

But Czech word order is more flexible than English, so other versions are possible depending on emphasis.

For example:

• Na stole jsou kuchyňské potřeby.
  = On the table are kitchen supplies.
  This puts more focus on where they are.

The meaning stays basically the same, but the emphasis changes.

A rough English-friendly guide would be:

• Kuchyňské ≈ koo-KHIN-skeh
• potřeby ≈ PO-trzheh-bih
• jsou ≈ ysoh
• na stole ≈ na STO-leh

A few important sounds:

• ch in Czech is like the ch in German Bach or Scottish loch
• ň is a soft n, a bit like ny
• ř is a special Czech sound, something like a mix of r and zh; learners usually need practice with it
• stress is usually on the first syllable of each word:
  • KU-chyň-ské
  • PO-tře-by
  • JSOU
  • NA
  • STO-le

That depends on what single item you mean, because kuchyňské potřeby is a collective plural phrase.

A literal singular would be:

• Kuchyňská potřeba je na stole.

Grammatically this is fine, and it means something like A kitchen necessity/item is on the table. But in real life, Czech would often use a more specific noun instead, such as:

• Nůž je na stole. = The knife is on the table.
• Hrnec je na stole. = The pot is on the table.

So the plural phrase is more natural when talking about a group of kitchen items.

No. That is an important point.

The noun potřeba often means need, but potřeby can also mean:

• supplies
• items
• necessities
• equipment

So in kuchyňské potřeby, translating it as kitchen needs would sound odd in English unless the context is very specific. In most cases, kitchen supplies, kitchen utensils, or kitchenware is more natural.