Pasagerul așteaptă bagajul de cală.

Because Romanian usually adds the definite article to the end of the noun.

• pasager = a passenger
• pasagerul = the passenger
• bagaj = baggage / luggage
• bagajul = the baggage / the luggage

So in this sentence, both nouns are definite:

• Pasagerul = the passenger
• bagajul = the baggage

This is very common in Romanian and is one of the first things English speakers notice.

Așteaptă is the present-tense form of the verb a aștepta, meaning to wait or to await.

Here it means:

• he/she waits for
• is waiting for

Because Romanian present tense can often cover both the simple present and the progressive idea, așteaptă can be understood as:

• waits for
• is waiting for

In this sentence, the subject is pasagerul, so așteaptă means the passenger waits / is waiting.

Because Romanian a aștepta usually takes a direct object.

English says:

• to wait for the baggage

But Romanian says more literally:

• to await the baggage

So:

• Pasagerul așteaptă bagajul = The passenger is waiting for the baggage

This is a very important difference from English. You normally do not add a separate word equivalent to for here.

De cală describes the type of baggage: baggage that goes in the cargo hold of a plane.

• cală = hold, cargo hold
• bagaj de cală = checked baggage / hold baggage

So bagajul de cală means:

• the checked baggage
• the hold baggage
• literally, the baggage of the hold

This structure is very common in Romanian:

• bagaj de mână = hand luggage / carry-on baggage
• sală de clasă = classroom
  and so on.

Because bagaj often works like a collective or mass noun, similar to luggage in English.

So Romanian can say:

• bagajul = the luggage / the baggage

Even if it refers to several physical items, the singular is still natural.

If you want to talk about individual pieces, Romanian can also use:

• bagajele = the pieces of luggage / the bags

But bagajul de cală is perfectly normal when speaking generally about checked luggage.

In Romanian, pe is often used before a direct object when that object is a person or something highly specific/animate.

Examples:

• Văd pasagerul. = I see the passenger.
• Îl văd pe pasager. = I see the passenger.
  (with stronger marking, especially for a person)

But bagajul is an inanimate thing, so pe is not used here:

• Pasagerul așteaptă bagajul de cală.

So the sentence is completely normal without pe.

A simple learner-friendly guide:

• așteaptă ≈ ush-TEAP-tuh
• cală ≈ KAH-luh

A few important sounds:

• ș sounds like English sh
• ă is a short central vowel, something like the final sound in sofa or comma
• ea in așteaptă sounds like ya / eah, depending on accent and speech

So:

• așteaptă has three parts: aș-teap-tă
• stress is on teap

Yes, Romanian word order is fairly flexible, although Pasagerul așteaptă bagajul de cală is the most neutral and natural order.

This standard order is:

• subject + verb + object

You may also hear different orders for emphasis, for example:

• Bagajul de cală îl așteaptă pasagerul.
  This puts emphasis on the checked baggage, but it is less neutral and usually needs the clitic îl.

For a learner, the safest version is definitely:

• Pasagerul așteaptă bagajul de cală.

Not exactly in form, even though it can feel similar in meaning.

Romanian often uses de + noun to describe the type, purpose, or category of something.

So:

• bagaj de cală is not mainly about possession
• it is more like hold baggage or baggage for the hold

This is why de cală sounds natural here. It functions more like a set expression describing a category of baggage.

Yes, you can, but it adds a nuance.

• Pasagerul așteaptă bagajul de cală = The passenger is waiting for the checked baggage
• Pasagerul își așteaptă bagajul de cală = The passenger is waiting for his/her own checked baggage

The little word își makes the baggage belong to the subject. Without it, the sentence is more neutral and simply states the action.

So the original sentence is perfectly correct; își is only needed if you want to stress that it is the passenger’s own baggage.