Die Personalabteilung erklärt mir die Gehaltsabrechnung.

Because erklären usually takes:

• the person receiving the explanation in the dative
• the thing being explained in the accusative

So in Die Personalabteilung erklärt mir die Gehaltsabrechnung:

• mir = to me or for me in function, but German uses the dative
• die Gehaltsabrechnung = the thing being explained, so it is accusative

A useful pattern is:

• jemand erklärt jemandem etwas
  = someone explains something to someone

Examples:

• Sie erklärt mir den Vertrag.
• Ich erkläre dir die Aufgabe.

They belong to two different nouns:

• Die Personalabteilung = the HR department
• die Gehaltsabrechnung = the payslip / salary statement

Both nouns are feminine, so their article is die in the nominative and also in the accusative singular.

That can look confusing at first, but the role of each noun is shown by word order and the verb:

• Die Personalabteilung is the subject
• die Gehaltsabrechnung is the direct object

In a normal German main clause, the subject often comes before the verb, and that is what happens here:

• Die Personalabteilung = subject
• erklärt = verb
• mir = indirect object
• die Gehaltsabrechnung = direct object

So the structure is:

• Subject + verb + dative object + accusative object

Also, semantically it makes sense: the HR department is doing the explaining.

Because the subject is Die Personalabteilung, which is third person singular.

The infinitive is erklären. Its present-tense forms include:

• ich erkläre
• du erklärst
• er/sie/es erklärt
• wir erklären
• ihr erklärt
• sie/Sie erklären

Since die Personalabteilung is singular, you use erklärt.

That is a very common word order in German when both objects are nouns/pronouns:

• dative pronoun often comes before
• full accusative noun phrase often comes later

So mir die Gehaltsabrechnung sounds very natural.

Compare:

• Die Personalabteilung erklärt mir die Gehaltsabrechnung.

This is one of the most typical orders.

A helpful guideline:

• pronouns often come earlier than full nouns

For example:

• Sie gibt mir das Formular.
• Er zeigt dir den Raum.

That version is generally not the normal choice.

German strongly prefers:

• Die Personalabteilung erklärt mir die Gehaltsabrechnung.

Putting mir at the end sounds unnatural in a neutral sentence.

If you change the order, you usually need a special reason such as emphasis, and even then other word orders are more likely than placing mir last.

It is a compound noun:

• Personal = personnel / staff
• Abteilung = department

Together:

• Personalabteilung = HR department / personnel department

The grammatical gender comes from the last part of the compound:

• die Abteilung is feminine
• therefore die Personalabteilung is also feminine

This is a very important rule in German compounds.

It is also a compound noun:

• Gehalt = salary
• Abrechnung = statement, settlement, calculation, accounting

Together:

• Gehaltsabrechnung = salary statement / payslip / payroll statement

Notice the -s- in the middle:

• Gehalt → Gehalts-

This linking -s- is common in German compounds, although it is not always predictable and often has to be learned with the word.

The gender comes from Abrechnung:

• die Abrechnung
• therefore die Gehaltsabrechnung is feminine too

In German, all nouns are capitalized, not just proper names.

So you write:

• Personalabteilung
• Gehaltsabrechnung

This is one of the most noticeable spelling differences between German and English.

Yes. In German, die Personalabteilung is a singular noun, so the verb is singular:

• Die Personalabteilung erklärt ...

English also often does this with words like the department or the team, although British and American English can differ sometimes with collective nouns. In German, you simply follow the grammatical number of the noun, which here is singular.

Yes. Since it is a dative pronoun, you can swap it for other dative forms:

• mir = to me
• dir = to you
• ihm = to him
• ihr = to her
• uns = to us
• euch = to you all
• ihnen = to them / to you (formal, depending on capitalization)

Examples:

• Die Personalabteilung erklärt dir die Gehaltsabrechnung.
• Die Personalabteilung erklärt uns die Gehaltsabrechnung.

Yes. The sentence sounds natural in an office or administrative context.

A few things make it feel formal or workplace-related:

• Personalabteilung is an institutional word
• Gehaltsabrechnung is administrative/business vocabulary
• erklären is neutral and standard

So this is exactly the kind of sentence you might hear in a company, during onboarding, or when asking HR about payroll.