Ο επιβάτης περιμένει κοντά στην πύλη μέχρι να αρχίσει η επιβίβαση.

Επιβάτης is a masculine noun, so it takes the masculine article ο in the nominative singular: ο επιβάτης.

Even though passenger in English is gender-neutral, Greek nouns have grammatical gender. If you specifically mean a female passenger, you may also hear η επιβάτισσα.

Περιμένει is the 3rd person singular present of περιμένω.

So it means he/she waits or he/she is waiting. In Greek, the present tense often covers both the simple present and the present continuous, and context tells you which English translation sounds best.

It can mean either.

Greek does not usually make the same sharp distinction English makes between waits and is waiting. In this sentence, English would often naturally say is waiting, but waits is also a possible translation depending on style.

Κοντά means near or close.

It can be used on its own, but very often it appears with σε plus a noun: κοντά στην πύλη = near the gate. So here it tells you where the passenger is waiting.

Στην is the contracted form of σε την.

This is extremely common in modern Greek:

• σε + τον = στον
• σε + τη(ν) = στη(ν)
• σε + το = στο

So στην πύλη literally comes from σε την πύλη.

The basic dictionary form is η πύλη because that is the nominative.

After σε, Greek normally uses the accusative, so η πύλη becomes την πύλη. That is why you get στην πύλη.

Yes. Πύλη is the normal word for a gate, especially in places like airports, ports, or stadiums.

Πόρτα usually means a door. So at an airport, πύλη is the natural choice for boarding gate.

Μέχρι means until/up to, but when Greek introduces a whole clause with a verb, it usually uses μέχρι να.

So:

• μέχρι το βράδυ = until the evening
• μέχρι να αρχίσει η επιβίβαση = until the boarding starts

In other words, μέχρι να is a very common pattern for until + verb.

After μέχρι να, Greek uses the subjunctive, and here the natural form is να αρχίσει, the aorist subjunctive of αρχίζω.

That form is used because this is a single event: the moment when boarding begins.
Να αρχίζει would suggest a more ongoing or repeated idea, which does not fit as well here.
And αρχίζει by itself is indicative, not the form normally used after μέχρι να.

Because η επιβίβαση is the subject of αρχίσει.

The structure is literally: until [the boarding] starts

Since the boarding is the thing doing the action of starting, it stays in the nominative: η επιβίβαση.

Greek uses the definite article more often than English.

Here η επιβίβαση refers to the specific boarding event for that flight, so the article sounds natural. In a full sentence like this, leaving it out would usually sound incomplete or unnatural.

Greek word order is more flexible than English because articles and case endings help show what each word is doing.

The given sentence is a very neutral, natural order: Ο επιβάτης περιμένει κοντά στην πύλη μέχρι να αρχίσει η επιβίβαση.

But Greek could move parts around for emphasis, for example: Κοντά στην πύλη περιμένει ο επιβάτης...

So the order can change, but the original version is the most straightforward one for a learner.