Die Gießkanne steht hinter der Vase auf dem Balkon.

Because the articles change for two different reasons: gender and case.

• Gießkanne is a feminine noun, and here it is the subject of the sentence, so it is in the nominative:

  • die Gießkanne

• Vase is also feminine, but it comes after hinter, and here hinter describes a location (not movement), so it takes the dative:

  • hinter der Vase

• Balkon is masculine, and auf also takes the dative here because it describes a location:

  • auf dem Balkon

So the cases are:

• die Gießkanne = nominative feminine
• der Vase = dative feminine
• dem Balkon = dative masculine

German often uses special position verbs where English would just use is.

Here, stehen means to stand and is commonly used for things that are upright or thought of as standing in a position, such as:

• bottles
• vases
• cans
• watering cans
• lamps

So:

• Die Gießkanne steht ... = The watering can is standing ...

In natural English, you would usually just say is, but in German, steht sounds more idiomatic here.

If you said Die Gießkanne ist hinter der Vase, it would not be wrong in every context, but steht is more natural because it describes the object’s physical position.

Because hinter is a two-way preposition.

Two-way prepositions can take:

• accusative when there is movement toward a destination
• dative when there is location or position

Here, the sentence describes where the watering can is, not where it is being moved. So German uses the dative:

• Die Gießkanne steht hinter der Vase.

Compare:

• Die Gießkanne steht hinter der Vase.
  = It is located behind the vase.
  → dative

• Ich stelle die Gießkanne hinter die Vase.
  = I put the watering can behind the vase.
  → accusative

For the same reason: auf is also a two-way preposition.

• auf dem Balkon = on / on the area of / at the balcony → location → dative
• auf den Balkon = onto the balcony → movement toward it → accusative

In your sentence, the watering can is already there, so German uses the dative:

• auf dem Balkon

Example contrast:

• Die Gießkanne steht auf dem Balkon.
  = The watering can is on the balcony.

• Ich stelle die Gießkanne auf den Balkon.
  = I put the watering can onto the balcony.

The sentence follows normal German main-clause word order:

• Die Gießkanne = subject
• steht = verb
• hinter der Vase = location phrase
• auf dem Balkon = another location phrase

So the pattern is roughly:

Subject + verb + details

German main clauses normally put the finite verb in second position. Here that gives:

• Die Gießkanne steht hinter der Vase auf dem Balkon.

You could also move another element to the front for emphasis, but then the verb still stays second:

• Auf dem Balkon steht die Gießkanne hinter der Vase.
• Hinter der Vase steht die Gießkanne auf dem Balkon.

That does not change the core meaning much, but it changes the emphasis.

This is a very good question, because the sentence can feel a little ambiguous when read by itself.

Die Gießkanne steht hinter der Vase auf dem Balkon.

This will usually be understood as:

• the watering can is behind the vase,
• and this whole scene is on the balcony.

So in practice, most people understand auf dem Balkon as giving the overall location.

But grammatically, a learner may wonder whether it could mean:

• the vase on the balcony

That is possible as a reading in isolation, because German often allows phrases to stack like this. Usually, context makes it clear.

If you want to remove ambiguity, you could say for example:

• Auf dem Balkon steht die Gießkanne hinter der Vase.
  This makes the balcony clearly the location of the whole scene.

Or:

• Die Gießkanne steht auf dem Balkon hinter der Vase.
  This also strongly suggests the whole scene is on the balcony.

Because in German, all nouns are capitalized, not just proper names.

So in this sentence:

• Gießkanne
• Vase
• Balkon

all begin with a capital letter because they are nouns.

This is one of the most noticeable differences from English spelling.

Gießkanne is a compound noun, which is very common in German.

It is made from:

• gießen = to pour / to water
• Kanne = jug, can

So Gießkanne literally means something like pouring can, which is why it means watering can.

A useful thing to know about German compounds is that the last part usually determines the grammatical gender. Since Kanne is feminine (die Kanne), the whole compound is also feminine:

• die Gießkanne

The letter ß is called Eszett or scharfes S.

In Gießkanne, it is pronounced like an s sound, roughly like ss in English. The word is pronounced approximately:

• Gießkanne → geess-kah-nuh
  more accurately: [giːsˌkanə]

A few helpful points:

• ie in German usually sounds like a long ee
• ß sounds like ss
• Gieß- therefore sounds like geess

In modern German spelling, ß often appears after a long vowel or diphthong.

Yes, you probably can, and people would understand you.

But steht is more idiomatic because German often prefers a position verb when talking about where an object is physically located.

So:

• Die Gießkanne ist hinter der Vase auf dem Balkon.
  = understandable

• Die Gießkanne steht hinter der Vase auf dem Balkon.
  = more natural German

This is similar to how German often uses:

• stehen for upright things
• liegen for things lying flat
• hängen for things hanging
• sitzen for people/animals sitting, and sometimes things in certain fixed positions

Because the article die can mean either:

• the for a feminine singular noun, or
• the for a plural noun

So you have to look at the noun form and the verb.

Here:

• Gießkanne is the singular form
• the verb is steht, which is singular

If it were plural, you would have:

• Die Gießkannen stehen hinter der Vase auf dem Balkon.

So steht helps confirm that die Gießkanne is singular.

Hinter means behind.

It describes position relative to something else, in this case:

• the watering can is behind the vase

Like English behind, it is a relational word: you understand the watering can’s position by comparing it to the vase.

Because it is a preposition of place, it often appears with a noun phrase:

• hinter der Vase
• hinter dem Haus
• hinter dem Tisch

And as mentioned earlier, it takes:

• dative for location
• accusative for movement toward that position