Learn Hardcore Greek: Ο επιβάτης περιμένει κοντά στην πύλη μέχρι να αρχίσει η επιβίβαση. - The male passenger waits near the gate until boarding begins.

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.

What form is περιμένει?

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.

Does περιμένει mean waits or is waiting?

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.

What does κοντά mean here?

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.