مجفف الشعر والشامبو في الجناح.

This is an iḍāfa construction, often called a genitive/possessive construction.

• مجفف = dryer
• الشعر = the hair

So literally, مجفف الشعر means dryer of the hair, which English naturally says as hair dryer.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun shows whether the whole phrase is definite

Because الشعر is definite, the whole phrase مجفف الشعر is understood as the hair dryer.

In Arabic, body parts and many generic nouns are often made definite where English would just use a general noun.

So:

• الشعر = the hair

In مجفف الشعر, Arabic is literally saying the dryer of the hair. Even though English says hair dryer without the, Arabic commonly uses the definite form here.

In Arabic, present-tense sentences often do not use an explicit verb meaning is/are.

So:

• مجفف الشعر والشامبو في الجناح means
• The hair dryer and the shampoo are in the suite/wing

This is called a nominal sentence. The idea of are is understood from the structure.

If you wanted past tense, you would normally use a verb such as كان:

• كان مجفف الشعر والشامبو في الجناح = The hair dryer and shampoo were in the suite

Yes, شامبو is a borrowed word, but borrowed nouns in Arabic can still take the definite article الـ.

So:

• شامبو = shampoo
• الشامبو = the shampoo

That is completely normal. Arabic treats many loanwords like regular nouns in this way.

الجناح literally means the wing. Depending on context, it can mean:

• a wing of a building
• a suite, especially in a hotel
• sometimes a special section, department, or pavilion

So in this sentence, the best translation depends on context. If this is about a hotel room, suite is likely. If it is about a larger building, wing may be better.

Yes. و simply means and.

So:

• مجفف الشعر والشامبو = the hair dryer and the shampoo

The sentence says that both of these items are في الجناح.

A simple breakdown is:

• مجفف الشعر والشامبو = the topic/subject part
• في الجناح = the predicate/location part

More specifically:

• مجفف = first noun of an iḍāfa
• الشعر = second noun of the iḍāfa, so it is in the genitive relationship
• الشامبو = coordinated with مجفف الشعر by و
• في = preposition, meaning in
• الجناح = object of the preposition في

So the sentence structure is basically:

[The hair dryer and the shampoo] + [are in the suite/wing]

Yes. In normal Arabic writing, short vowels and most case endings are usually not written.

A fully vocalized version would look something like:

مُجَفِّفُ الشَّعْرِ وَالشَّامْبُو فِي الجَنَاحِ

What those endings show:

• مجففُ: nominative, because it is part of the subject/topic
• الشعرِ: genitive, because it is the second part of an iḍāfa
• الجناحِ: genitive, because it comes after في

In everyday reading, learners usually rely on grammar and context rather than written case endings.

A careful pronunciation is approximately:

mujaffifu sh-shaʿri wa-sh-shāmbū fī l-janāḥ

A few useful notes:

• الـ in الشعر is pronounced ash- / sh- here, because ش is a sun letter, so the l sound assimilates.
• ع in شعر is a consonant that has no exact English equivalent.
• ح in جناح is a stronger, breathier h than English h.

If you pause at the end of the sentence in natural speech, final case vowels are often not pronounced clearly.

Yes. Arabic word order is flexible.

For example, you could also say:

في الجناح مجفف الشعر والشامبو

This still means essentially the same thing, but it puts more focus on the location first:

• In the suite/wing, there are the hair dryer and the shampoo

The original version is perfectly natural, though, especially if the items are the main topic.