Meine Nichte lacht, weil der Hund seinen Schwanz im Kreis bewegt.

Because weil introduces a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

So:

• main clause: Meine Nichte lacht
• subordinate clause: weil der Hund seinen Schwanz im Kreis bewegt

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

Compare:

• Der Hund bewegt seinen Schwanz im Kreis.
• ..., weil der Hund seinen Schwanz im Kreis bewegt.

In the second version, bewegt moves to the end because of weil.

In German, subordinate clauses are normally separated from the main clause by a comma. Since weil der Hund seinen Schwanz im Kreis bewegt is a subordinate clause, the comma is required.

So the structure is:

• Meine Nichte lacht, = main clause
• weil der Hund seinen Schwanz im Kreis bewegt. = subordinate clause

This comma is not optional in standard German.

Because der Hund is the subject of the weil clause — the dog is the one doing the action.

In that clause:

• der Hund = nominative subject
• seinen Schwanz = accusative object

A quick test is to ask Who is moving the tail?
Answer: der Hund. So it must be nominative.

Seinen Schwanz is in the accusative because it is the direct object of bewegt.

The verb bewegen here takes an object:

• der Hund moves something
• that something is seinen Schwanz

Since Schwanz is masculine (der Schwanz), its accusative form is:

• der Schwanz → den Schwanz

And the possessive determiner changes with it:

• sein Schwanz → seinen Schwanz

So seinen Schwanz means his tail in the accusative masculine form.

In a way, it does both — but in different ways.

• The base form sein- shows who the owner is: a masculine or neuter possessor, here der Hund
• The ending -en agrees with the noun being described: Schwanz, which is masculine accusative here

So:

• sein- = his / its
• -en = because Schwanz is masculine accusative

That is why you get seinen Schwanz.

Yes. German sein can mean either his or its, depending on what it refers to.

Here it refers to der Hund, and in English we often say its tail for an animal, though his tail is also possible if the dog is thought of as male.

So grammatically, German uses sein- because Hund is a masculine noun. That does not always mean the English translation has to be his in a biological sense.

Im Kreis is a contraction of in dem Kreis.

• in dem → im

Here im Kreis means something like:

• in a circle
• in circles
• around in a circular motion

It is an idiomatic expression. In this sentence it describes how the tail is moving.

Because this phrase describes location or manner, not movement into something.

German in can take:

• dative for location/state
• accusative for direction/change toward something

Here the tail is moving in a circular pattern, not moving into a circle, so German uses the dative:

• im Kreis = in the circle / in circles

If it were truly directional, you might see accusative, but not in this expression.

Yes. German main clauses are flexible, but the conjugated verb still has to stay in the second position.

The sentence as given starts with the subject:

• Meine Nichte lacht, weil ...

You could also start with the weil clause:

• Weil der Hund seinen Schwanz im Kreis bewegt, lacht meine Nichte.

That is also correct. Notice that in the main clause after the subordinate clause, the verb still comes first within the clause:

• ..., lacht meine Nichte not
• ..., meine Nichte lacht

This is the usual verb-second rule in main clauses.

Because lacht is the correct 3rd person singular present-tense form of lachen.

Conjugation:

• ich lache
• du lachst
• er/sie/es lacht
• wir lachen
• ihr lacht
• sie/Sie lachen

Since meine Nichte is singular and equivalent to sie, the correct form is lacht.

Yes. Here bewegen is transitive, meaning it takes a direct object:

• Der Hund bewegt seinen Schwanz.
• The dog moves its tail.

By contrast, sich bewegen means to move oneself / to be in motion:

• Der Hund bewegt sich.
• The dog is moving.

So:

• bewegen + object = move something
• sich bewegen = move oneself

In your sentence, the dog is moving its tail, so the transitive use is needed.

It is grammatical and easy to understand. However, in everyday German, a more idiomatic verb for a dog moving its tail is often wedeln.

For example:

• Meine Nichte lacht, weil der Hund mit dem Schwanz wedelt.

That said, seinen Schwanz im Kreis bewegt is still perfectly understandable and emphasizes the circular motion more literally.