يتحرك الطفل في الغرفة.

Because verb–subject–prepositional phrase is a very common word order in Modern Standard Arabic.

So:

• يتحرك = moves / is moving
• الطفل = the child
• في الغرفة = in the room

This makes the sentence a verbal sentence.

Arabic can also say:

• الطفل يتحرك في الغرفة

That version is also correct, but it shifts the feel a bit toward The child is moving in the room, with more focus on the child as the topic.
The original version is the more neutral, standard verbal pattern.

يتحرك is the imperfect (non-past) form of the verb تحرّك.

In context, it can mean:

• moves
• is moving
• sometimes does move, depending on context

Arabic imperfect verbs often cover both the simple present and the present progressive in English.

So يتحرك الطفل could mean either:

• The child moves
• The child is moving

The surrounding context usually tells you which English translation is best.

The يـ at the beginning is the marker for third person masculine singular in the imperfect verb.

So يتحرك means:

• he moves
• he is moving

This matches الطفل, because الطفل is:

• singular
• masculine

If the subject changed, the verb form would change too. For example:

• تتحرك الطفلة = The girl is moving
• يتحرك الأطفال = The children are moving (with a masculine plural subject after the verb, the verb often stays singular in standard VSO structure)

In this sentence, the subject is الطفل, which is singular masculine, so the singular masculine verb يتحرك is exactly what you expect.

More generally, Arabic agreement depends partly on word order:

• If the verb comes before the subject, Arabic often uses partial agreement
• If the subject comes before the verb, Arabic usually uses full agreement

For this sentence, since the subject is singular anyway, there is no visible difference to worry about.
But this becomes more important with plural subjects.

الـ is the Arabic definite article, meaning the.

So:

• طفل = a child / child
• الطفل = the child

In your sentence, الطفل is specific: the child.

Also, because the noun is definite, it does not take tanwīn (the -n ending that often marks indefiniteness).

Because في means in.

So:

• في = in
• الغرفة = the room

Together:

• في الغرفة = in the room

Arabic uses prepositions much like English does here.
Without في, the meaning would change completely, and الغرفة would no longer mean in the room.

Because في is a preposition, and nouns after prepositions are normally in the genitive case in Arabic.

So in fully vowelled Arabic, you would write:

• في الغرفةِ

That final ـِ is the genitive ending.

Likewise, الطفل would be الطفلُ in full vocalization, because it is the subject and therefore nominative.

In normal everyday Arabic writing, those short case endings are usually not written, so you often just see:

• يتحرك الطفل في الغرفة

The final ة is called tā’ marbūṭa.

When you stop at the word by itself, it is usually pronounced like -a:

• الغرفة → al-ghurfa

But in fully pronounced grammatical speech, when followed by a case ending, it is pronounced with a t sound:

• في الغرفةِ → fī al-ghurfati

So both ideas are important:

• pause form: al-ghurfa
• fully inflected grammatical form: al-ghurfati

Learners often first hear the pause form more often in practice.

It comes from the root ح ر ك, which is connected with the idea of movement.

The verb here is from Form V:

• past: تحرّك = moved / became in motion
• imperfect: يتحرك = moves / is moving

This is useful because many Arabic words are built from roots and patterns.
If you learn the root ح ر ك, you may also notice related words, such as ones connected with motion or movement.

Because Arabic does not need an auxiliary verb like English is in this kind of sentence.

English often uses:

• The child is moving

But Arabic can simply use the imperfect verb:

• يتحرك الطفل

That already includes the idea of present action, depending on context.

So Arabic does not need a separate present-tense is here.

Yes. The Arabic imperfect is flexible.

يتحرك الطفل في الغرفة can mean:

• The child is moving in the room
• The child moves in the room

Which one sounds best depends on context:

• If you are describing what is happening right now, is moving is natural.
• If you are describing a habitual action, moves may fit better.

This is very common in Arabic: one verb form often covers meanings that English splits into two different tenses.

Yes, but it means something different.

• الطفل في الغرفة = The child is in the room
• يتحرك الطفل في الغرفة = The child is moving in the room

So the first sentence describes location only.
The second sentence describes action + location.

This is a useful contrast because it shows how Arabic can express either:

• a noun phrase with a prepositional phrase: الطفل في الغرفة
• or a full action with a verb: يتحرك الطفل في الغرفة