Unsere Katze miaut laut, weil ihr Napf leer ist.

Because Katze is a feminine noun in German: die Katze.

The possessive unser changes its ending to match the gender, number, and case of the noun that follows it. In the nominative singular feminine, it becomes unsere.

So:

• unser Hund = our dog
• unsere Katze = our cat
• unser Kind = our child

Here, Katze is the subject of the sentence, so nominative is used.

Miaut is the 3rd person singular form of the verb miauen, which means to meow.

So:

• ich miaue = I meow
• du miaust = you meow
• er/sie/es miaut = he/she/it meows

Since unsere Katze is a singular subject, German uses miaut.

Laut here means loudly.

In German, words like laut, schnell, gern, and many others can function adverbially without needing a special -ly ending like in English.

So:

• Die Katze miaut laut. = The cat meows loudly.
• Er spricht leise. = He speaks quietly.
• Sie fährt schnell. = She drives quickly.

The position is natural here: verb + adverb.

Because weil introduces a subordinate clause.

In German, subordinate clauses are separated from the main clause by a comma.

So the sentence has two parts:

• Unsere Katze miaut laut = main clause
• weil ihr Napf leer ist = subordinate clause

That is why the comma is required.

Because weil is a subordinating conjunction, and in German, subordinating conjunctions usually send the conjugated verb to the end of the clause.

Compare:

• Main clause: Ihr Napf ist leer.
• After weil: weil ihr Napf leer ist

This is one of the most important word-order patterns in German.

Other examples:

• Ich bleibe zu Hause, weil ich müde bin.
• Sie lernt Deutsch, weil sie in Berlin arbeitet.

Yes, here ihr means her and refers to unsere Katze.

So ihr Napf means her bowl.

German possessives agree with the noun being possessed, not with the owner in the way English learners sometimes expect. Since Napf is masculine and here in the nominative singular, the form is ihr.

Compare:

• ihr Napf = her bowl
• ihre Katze = her cat
• ihre Näpfe = her bowls

In this sentence, Napf is the subject of the clause ihr Napf leer ist, so nominative is needed.

Yes, ihr can also mean their, depending on context.

For example:

• ihr Napf can mean her bowl
• ihr Napf can also mean their bowl

Here, though, the meaning is clearly her bowl, because it refers back to our cat.

German often relies on context to distinguish these meanings.

Napf is a very common word for an animal’s food or water bowl.

A Schüssel is more like a general bowl used by people, for food, mixing, serving, and so on.

So if you are talking about a cat’s bowl, Napf sounds much more natural.

Examples:

• der Futternapf = food bowl
• der Wassernapf = water bowl
• der Napf = bowl, usually for a pet

Because leer is a predicate adjective here, not an adjective directly in front of a noun.

In German:

• If an adjective comes before a noun, it takes an ending
  
  • ein leerer Napf
• If it comes after a form of sein, werden, bleiben, it usually has no ending
  
  • Der Napf ist leer

So in ihr Napf leer ist, leer stays in its basic form.

Yes, grammatically you can.

• weil der Napf leer ist = because the bowl is empty
• weil ihr Napf leer ist = because her bowl is empty

The version with ihr is more specific because it clearly connects the bowl to the cat.

If the context already makes it obvious whose bowl it is, der Napf could also work.

Miaut is pronounced roughly like mee-owt.

A few helpful points:

• mi sounds like mee
• au sounds like the ow in now
• the final t is clearly pronounced

So the word has a sound close to the noise a cat makes, which is fitting.

Yes. You can say:

Weil ihr Napf leer ist, miaut unsere Katze laut.

That is also correct.

When the subordinate clause comes first, the main clause still follows the normal German rule that the conjugated verb comes in second position. So you get:

• Weil ihr Napf leer ist,
• miaut unsere Katze laut.

Both versions are natural; the difference is mainly one of emphasis and style.