هذا مدير القسم.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is / are / am.

So:

• هذا مدير القسم = This is the department manager

If you wanted the past or future, then Arabic would use a verb, but in the present tense it is normally omitted.

هذا means this and is a demonstrative.

In this sentence, it stands on its own, almost like saying:

• This [person] is the department manager

So هذا is not directly attached to a noun here. It is acting like the subject of the sentence: this.

Because it refers to a masculine singular person: مدير (manager/director), which is grammatically masculine.

If the person were feminine, you would normally say:

• هذه مديرة القسم = This is the department manager (female)

So the demonstrative should match the gender and number of the person being pointed out.

Yes. هذا can refer to a person or a thing.

So it can mean:

• this man
• this person
• this thing

The exact meaning depends on context. In your sentence, it clearly refers to a person.

Because مدير القسم is an iḍāfa construction, often called a genitive construction or annexation.

This structure is very common in Arabic and usually works like:

• X of Y
• or the Y’s X

So:

• مدير القسم = manager of the department = the department manager

In an iḍāfa:

• the first noun usually does not take ال
• the second noun can be definite with ال

That is why you say مدير القسم, not المدير القسم.

Because in an iḍāfa, the definiteness of the whole phrase is determined by the second noun.

Here:

• القسم = the department (definite)
• therefore مدير القسم = the manager of the department / the department manager (also definite)

So even though مدير does not have ال, the whole phrase is definite because it is linked to a definite noun.

Because مدير is the first word in an iḍāfa construction, and the first noun in an iḍāfa:

• does not take ال
• does not take tanwīn

So you get:

• مدير القسم

not:

• مديرٌ القسم
• المدير القسم

This is one of the clearest signs that a noun is functioning as the first part of an iḍāfa.

القسم means the department (or sometimes the section, depending on context).

Inside مدير القسم, it is the second term of the iḍāfa, the noun that tells you manager of what?

So:

• مدير = manager
• القسم = the department
• مدير القسم = manager of the department

A careful pronunciation with full case endings is:

• hādhā mudīru l-qismi

In pause, which is how people often cite or read it more simply, you will often hear:

• hādhā mudīr al-qism

A few notes:

• مدير = mudīr
• القسم = al-qism
• the q in qism is ق, a deeper sound than English k

In fully inflected MSA, the analysis is:

• هذا — an indeclinable demonstrative, functioning as the subject
• مديرُ — nominative, because it is the predicate of the sentence
• القسمِ — genitive, because it is the second noun in an iḍāfa

So the full form is:

• هذا مديرُ القسمِ

In normal pause, the short final vowels are often not pronounced, so learners often hear:

• هذا مدير القسم

Yes. هذا هو مدير القسم is also correct.

Adding هو can give extra clarity or emphasis, something like:

• This is the department manager
• This here is the department manager

But the simpler and more basic version is:

• هذا مدير القسم

The meaning changes.

• هذا مدير القسم = This is the department manager
• مدير القسم هذا = this department manager

In the first sentence, هذا stands alone as this.
In the second, هذا comes after the noun phrase and directly describes it: this department manager.

That word-order difference is very important in Arabic.