التكرارات مهمة للياقة البدنية في هذا البرنامج.

Because this is a nominal sentence in the present tense. In Arabic, the verb to be is usually not expressed in present-tense statements like this.

So:

• التكرارات = repetitions
• مهمة = important

Together, التكرارات مهمة means repetitions are important.

If you wanted a past or future meaning, Arabic would normally use an actual verb, such as كانت for was/were or ستكون for will be.

This is a very common Arabic pattern.

التكرارات is a non-human plural, and in Modern Standard Arabic, non-human plurals usually take feminine singular agreement in adjectives and verbs.

So:

• التكرارات = repetitions (plural)
• مهمة = important (feminine singular)

This is grammatically normal in MSA.

Compare:

• الكتب مفيدة = the books are useful
  
  • الكتب is plural, but مفيدة is feminine singular

If the plural referred to people, the adjective would usually be plural too.

التكرارات means repetitions or repeats. In a fitness context, it can often mean reps.

Its singular is تكرار, meaning repetition.

So:

• تكرار = a repetition
• تكرارات = repetitions

This plural uses the ending -ات, which is very common in Arabic, especially for abstract or non-human nouns.

Arabic often uses الـ to speak about something in a general or class-wide sense.

So التكرارات مهمة can mean:

• repetitions are important
• or more literally the repetitions are important

In English, generic statements often omit the, but Arabic frequently uses الـ in that role.

Without الـ, تكرارات مهمة would sound more indefinite, more like:

• some important repetitions
• or important repetitions

So the definite article here is quite natural.

This phrase breaks down like this:

• لِـ = for
• اللياقة = fitness
• البدنية = physical / bodily

So للياقة البدنية means for physical fitness.

A few important grammar points:

1. البدنية is an adjective describing اللياقة.
2. In Arabic, adjectives usually come after the noun.
3. The adjective agrees with the noun in definiteness, gender, and number.

So:

• اللياقة is feminine singular and definite
• therefore البدنية is also feminine singular and definite

Literally, the phrase is something like for the fitness physical, but natural English is for physical fitness.

Because لِـ is a prefix preposition in Arabic. It attaches directly to the following word.

So:

• لِ
  • اللياقة becomes للياقة

This is completely normal with short prepositions such as:

• بِـ = with / by
• لِـ = for / to
• كَـ = like / as

Also, when one of these attaches to a word beginning with الـ, the writing and pronunciation contract.

So للياقة is just the normal written form of for the fitness.

Because برنامج is a masculine noun.

So the correct demonstrative is:

• هذا البرنامج = this program

If the noun were feminine, you would use:

• هذه = this (for feminine nouns)

For example:

• هذه الخطة = this plan

So here, هذا matches برنامج correctly.

The sentence is:

التكرارات مهمة للياقة البدنية في هذا البرنامج.

A word-for-word breakdown is:

• التكرارات = repetitions
• مهمة = important
• للياقة البدنية = for physical fitness
• في هذا البرنامج = in this program

So the structure is:

• subject: التكرارات
• predicate/adjective: مهمة
• then two prepositional phrases:
  • للياقة البدنية
  • في هذا البرنامج

A very literal translation would be:

Repetitions [are] important for physical fitness in this program.

Yes, Arabic word order is somewhat flexible, especially with prepositional phrases.

The original sentence is straightforward and neutral:

• التكرارات مهمة للياقة البدنية في هذا البرنامج

But you could also front the setting for emphasis, for example:

• في هذا البرنامج، التكرارات مهمة للياقة البدنية

That would mean the same thing, but with extra emphasis on in this program.

The version you were given is a very natural neutral order.

A fully vocalized MSA version would be:

التَّكْرَارَاتُ مُهِمَّةٌ لِلَّيَاقَةِ الْبَدَنِيَّةِ فِي هَذَا الْبَرْنَامَجِ

A rough pronunciation is:

at-takrārātu muhimmatun lil-liyāqati al-badaniyyati fī hādhā al-barnāmaji

A few pronunciation notes:

• التكرارات begins with ت, a sun letter, so ال is pronounced as at-, not al-
• مهمة has a doubled m sound
• للياقة has a strong l sound because of the attached لِـ and the word beginning with ل

In normal speech, final case endings are often not pronounced, so it may sound more like:

at-takrārāt muhimma lil-liyāqa al-badaniyya fī hādhā al-barnāmaj

Yes. You could also say:

التكرار مهم للياقة البدنية في هذا البرنامج

That would mean something like:

Repetition is important for physical fitness in this program

The difference is mostly one of emphasis:

• التكرار = repetition as a general concept
• التكرارات = repetitions / reps as countable units

In a workout or exercise context, التكرارات is especially natural because it suggests actual counted repetitions.