اللياقة البدنية مهمة لصحة صديقي.

Because Arabic adjectives normally follow the noun they describe.

So:

• اللياقة = fitness
• البدنية = physical / bodily

Together, اللياقة البدنية literally looks like fitness physical, but in natural English it means physical fitness.

Also, the adjective must agree with the noun in:

• definiteness
• gender
• number
• usually case as well

That is why both words have الـ here.

Because البدنية is an adjective describing اللياقة, and in Arabic adjectives match the noun in definiteness.

• اللياقة البدنية = the physical fitness / physical fitness
• If you removed الـ from البدنية, it would sound grammatically wrong in standard Arabic here.

So this is a normal noun + adjective combination:

• اللياقة = the fitness
• البدنية = the physical

Because مهمة here is the predicate of the sentence, not an adjective attached directly to اللياقة البدنية.

The structure is:

• اللياقة البدنية = the subject/topic
• مهمة = important
• لصحة صديقي = for my friend’s health

So the sentence means:

• Physical fitness is important for my friend’s health.

If you said اللياقة البدنية المهمة, that would mean something more like:

• the important physical fitness

That would no longer be a complete sentence by itself.

Because it refers back to اللياقة, and لياقة is a feminine singular noun.

In Arabic, predicate adjectives agree with the noun they describe in gender and usually number.

So:

• masculine: مهم
• feminine: مهمة

Since اللياقة البدنية is feminine singular, the correct form is مهمة.

Because in Arabic, the verb to be is usually omitted in the present tense.

So Arabic often says:

• اللياقة البدنية مهمة
  literally: Physical fitness important

But the meaning is:

• Physical fitness is important

This is called a nominal sentence.

If you wanted the past tense, Arabic would use a verb, for example:

• كانت اللياقة البدنية مهمة = Physical fitness was important

The لِـ here is a preposition meaning for (sometimes to depending on context).

So:

• لصحة = for the health of...

It is attached directly to the following noun, which is very normal in Arabic.

Breakdown:

• لِ = for
• صحة = health

So لصحة صديقي means for my friend’s health.

Because صحة is the first word in an iḍāfa (construct phrase), which is how Arabic often expresses possession.

Here:

• صحة صديقي = my friend’s health

In an iḍāfa:

1. the first noun usually does not take الـ
2. the first noun also does not take tanwīn
3. the second part shows who owns or specifies the first noun

So صحة صديقي literally means:

• health of my friend

صديقي is made of:

• صديق = friend
• ـي = my

So:

• صديقي = my friend

This ـي is a possessive suffix attached directly to the noun.

Other examples:

• كتابي = my book
• بيتي = my house
• أستاذي = my teacher

It is an iḍāfa phrase, often called a construct phrase.

Its pattern is:

• noun + noun/pronoun relationship

Here:

• صحة = health
• صديقي = my friend

So the whole phrase means:

• my friend’s health
• literally: the health of my friend

This is one of the most common structures in Arabic.

The ة is called tāʾ marbūṭa.

In this sentence, it behaves a little differently depending on position:

• مهمة at the end is usually pronounced muhimma (or muhimmah in careful pause)
• البدنية is usually al-badaniyya
• صحة inside صحة صديقي is pronounced with a t sound because it is in an iḍāfa:
  • ṣiḥḥat ṣadīqī

So this part is pronounced more like:

• ṣiḥḥat ṣadīqī = my friend’s health

That t sound in iḍāfa is very important to notice.

Because of the definite article الـ plus the first letter of the word.

The word begins with ل, and ل is a sun letter, so the ل of الـ assimilates to it.

So اللياقة is pronounced roughly:

• al-liyāqa with a doubled l sound

By contrast, in البدنية, the ب is a moon letter, so the ل of الـ is pronounced normally:

• al-badaniyya

So the two الـ words behave differently in pronunciation.

The sentence can be divided like this:

• اللياقة البدنية = subject/topic
• مهمة = predicate
• لصحة صديقي = prepositional phrase explaining what it is important for

So literally it is:

• Physical fitness — important — for my friend’s health

That is a very common Arabic sentence pattern.

A fully vocalized version could be written as:

• اللياقةُ البدنيةُ مهمةٌ لصحةِ صديقي

This shows the grammar more clearly:

• اللياقةُ = nominative
• البدنيةُ = agrees with it
• مهمةٌ = nominative predicate
• صحةِ = genitive after لِـ

In normal everyday Arabic writing, these short vowels are usually omitted.