Die Mutter schnallt das Kind an.

Because the full verb is anschnallen, which is a separable verb.

In a normal main clause, German often splits separable verbs:

• Die Mutter schnallt das Kind an.

The conjugated part goes in the usual verb position, and the prefix goes to the end.

Other examples:

• Ich mache die Tür auf. = I open the door.
• Er ruft mich an. = He calls me.

So here:

• anschnallen = to fasten / buckle in
• schnallt = the conjugated verb part
• an = the separable prefix

The base form is anschnallen.

Here is how it breaks down:

• an- = separable prefix
• schnallen = to fasten / buckle

In this sentence, schnallt is the 3rd person singular present tense form, used with die Mutter:

• ich schnalle an
• du schnallst an
• er/sie/es schnallt an

So Die Mutter schnallt ... an means The mother buckles ... in.

Because Mutter is a feminine noun in German.

German nouns have grammatical gender:

• der = masculine
• die = feminine
• das = neuter

So:

• die Mutter = the mother

This is true even though the person is female in real life; in this case, grammatical gender and natural gender match.

Because Kind is a neuter noun in German.

So the correct article is:

• das Kind = the child

This is something learners simply need to memorize with the noun:

• das Kind
• plural: die Kinder

Even though a child can be a boy or a girl, the noun Kind is grammatically neuter.

Because Kind is the direct object here, so it is in the accusative case. But for many neuter nouns, the article das stays the same in both nominative and accusative.

Compare:

• Nominative: das Kind spielt.
  = the child plays

• Accusative: Die Mutter sieht das Kind.
  = the mother sees the child

So in your sentence:

• Die Mutter = subject
• das Kind = direct object

It is accusative, but it still looks like das Kind.

You can tell from both meaning and verb agreement.

• Die Mutter is doing the action.
• das Kind is receiving the action.

Also, the verb schnallt is singular and matches die Mutter.

So the structure is:

• Die Mutter = subject
• schnallt = verb
• das Kind = object
• an = separable prefix

English uses word order very strongly to show this. German also uses word order, but cases help too.

Because an is the separable prefix of anschnallen.

In a main clause, German sends the prefix to the end:

• Die Mutter schnallt das Kind an.

But in some other structures, the verb stays together:

• Sie will das Kind anschnallen.
• Das Kind ist angeschnallt.

So:

• main clause: schnallt ... an
• infinitive or participle forms: anschnallen, angeschnallt

Not by itself, at least not in a way you can translate word-for-word in this sentence.

Although an can sometimes mean things like at, on, or to, here it is mainly functioning as part of the verb anschnallen.

So it is better to learn:

• anschnallen = to fasten / buckle up / buckle in

rather than trying to translate schnallen and an separately every time.

Here it means something like:

• to buckle the child in
• to fasten the child into a seat
• to strap the child in

It is often used for:

• seat belts
• car seats
• safety straps

So Die Mutter schnallt das Kind an would commonly describe a mother fastening a child into a car seat or with a seat belt.

Because in German main clauses, the finite verb usually goes in second position. This is often called the V2 rule.

In your sentence:

• Die Mutter = first element
• schnallt = second-position finite verb
• das Kind = next element
• an = separable prefix at the end

So the sentence follows a very standard German pattern.

Yes, German allows some flexibility, but the finite verb still usually stays in second position.

For example:

• Das Kind schnallt die Mutter an.
  This changes the meaning: The child buckles the mother in.

• Das Kind schnallt die Mutter an is grammatically possible, but it means something different because the subject has changed.

You could also front other elements in different contexts, but then the verb still stays second:

• Das Kind schnallt die Mutter an = different meaning
• An schnallt die Mutter das Kind = not correct in normal German

So for this meaning, Die Mutter schnallt das Kind an is the natural basic word order.

With the infinitive, the verb stays together:

• anschnallen

With a modal verb:

• Die Mutter will das Kind anschnallen.
  = The mother wants to buckle the child in.

Notice that after a modal verb, the infinitive goes to the end and is not split.

This is a very common pattern in German:

• Ich muss aufstehen.
• Sie kann mich anrufen.
• Die Mutter will das Kind anschnallen.