A nő a gyerekért siet, mert a metró hamarosan indul.

A is the Hungarian definite article, meaning the. Hungarian uses a before consonant-initial words and az before vowel-initial words. So:

• a nő = the woman
• a gyerekért = for the child
• a metró = the metro

Gyerekért is gyerek + -ért.

The suffix -ért often means for. It can express:

• doing something for someone
• going to get someone
• sometimes because of something

In this sentence, a gyerekért siet most naturally means she is hurrying for the child, in the sense of to get / pick up the child.

Because a gyerekért is not a direct object. It is a noun with the suffix -ért, which gives it the meaning for the child.

If you used a gyereket, that would be the accusative form, meaning the child as a direct object. But siet does not take gyerek here as a direct object; the idea is hurry for / hurry to get the child.

Not with the same meaning.

• a gyerekhez means to the child, emphasizing movement toward the child
• a gyerekért means for the child / to get the child

So siet a gyerekhez would mean she is hurrying to the child, while siet a gyerekért suggests she is hurrying to fetch the child or for the child's sake.

Siet means hurries / is hurrying. It is an intransitive verb here, so it does not have a direct object.

That matters because Hungarian definite conjugation is used with transitive verbs that take a definite direct object. Here a gyerekért is not a direct object, so the normal form siet is used.

Yes, A nő siet a gyerekért is also possible.

Hungarian word order is flexible and often reflects topic and focus, not just basic grammar. Putting a gyerekért right before the verb gives that part more prominence. A version with siet earlier can sound a bit more neutral, depending on context.

Mert means because. It introduces the reason:

• A nő a gyerekért siet = the main statement
• mert a metró hamarosan indul = the reason

So the second clause explains why she is hurrying.

Because Hungarian very often uses the present tense for the near future, especially when there is a time word such as hamarosan meaning soon.

So a metró hamarosan indul literally uses present tense, but in English it is often best translated as the metro is leaving soon or the metro will leave soon.

Hamarosan means soon / shortly.

In this sentence, a metró hamarosan indul is a very natural order. Hungarian allows some flexibility, so other placements are possible, but this version sounds normal and clear.

Both can refer to starting to leave or depart.

• indul = leaves / departs / starts
• elindul = often feels a bit more like sets off or starts off

With transport, indul is very common when talking about scheduled departure, so a metró hamarosan indul sounds very natural.

They are very close in meaning: both mean child.

• gyerek is the common everyday word
• gyermek is a bit more formal or official

In normal spoken Hungarian, gyerek is extremely common.