Amikor a gyerek alszik, az ajtó mindig be van csukva.

Amikor means when and introduces a time clause.

So Amikor a gyerek alszik means when the child is sleeping / when the child sleeps.

It is used here because the sentence describes the time when the main situation is true. This is different from ha, which means if and introduces a condition.

• amikor = when
• ha = if

So this sentence is about time, not condition.

Because Amikor a gyerek alszik is a subordinate clause, and it is followed by the main clause.

Hungarian normally separates this kind of clause with a comma:

• Amikor a gyerek alszik, az ajtó mindig be van csukva.

This is very similar to English:

• When the child is asleep, the door is always closed.

A gyerek uses the definite article, so it usually means the child.

In context, this normally refers to:

• a specific child already known to the speaker and listener, or
• a child understood from the situation, such as the baby, the kid, etc.

If it were egy gyerek, that would mean a child / one child, introducing a less specific child.

Hungarian often uses the definite article in places where English might be slightly more flexible.

Because the sentence describes a general or habitual situation:

• Whenever the child sleeps, the door is always closed.

Hungarian uses the present tense here just as English often does in similar statements about routine or repeated events.

So alszik does not have to mean only is sleeping right now. It can also mean sleeps in a general sense.

Be van csukva is a very common Hungarian structure meaning is closed / is shut.

It is made of three parts:

• be = a verbal prefix, here suggesting closed inward / shut
• van = is
• csukva = a participle-like form meaning closed/shut

Literally, it is something like is shut closed, but natural English is simply:

• is closed
• is shut

This structure focuses on the state/result of the door, not the action of someone closing it.

Because in this kind of construction, the verbal prefix is placed before van, while the participle stays after it:

• be van csukva

This is normal Hungarian word structure in result-state expressions.

Compare similar patterns:

• ki van nyitva = is open
• meg van írva = is written
• el van törve = is broken

So although be belongs semantically with csukva, it appears before van in the sentence.

Yes, csukva van is possible and means is closed/shut.

But be van csukva is often more explicit and idiomatic when talking about a door being shut closed.

There is a small nuance:

• csukva van = is closed
• be van csukva = is shut, closed up

In many everyday situations, the difference is small, but be van csukva sounds very natural for doors, windows, lids, and similar things.

Az ajtó means the door.

The article is definite because the speaker has a particular door in mind, usually one that is obvious from the context, such as the child's room door or the main door of the room.

Hungarian uses definite articles very regularly, so az ajtó is exactly what you would expect here.

Mindig means always.

Here it modifies the main predicate:

• az ajtó mindig be van csukva
• the door is always closed

Its position is natural because az ajtó is the topic, and then mindig comes before the rest of the predicate.

Hungarian word order is flexible, but this version is neutral and natural.

Yes, Hungarian word order is flexible, but changing it usually changes the emphasis.

The given sentence is a neutral version:

• Amikor a gyerek alszik, az ajtó mindig be van csukva.

Possible alternatives include:

• Amikor a gyerek alszik, mindig be van csukva az ajtó.
• Az ajtó mindig be van csukva, amikor a gyerek alszik.

These are still understandable, but they may sound slightly different in emphasis or information flow. The original sentence is a very standard way to say it.

It describes a state.

• a gyerek alszik = the child is sleeping
• az ajtó be van csukva = the door is in a closed state

So the sentence is not saying someone closes the door whenever the child sleeps. It says that during that time, the door is closed.

If you wanted to emphasize the action of closing, Hungarian would use a different structure, for example with a full verb meaning someone closes the door.

It is similar in meaning in some situations, but it is not exactly the same thing as the English passive.

English might say:

• The door is closed.

Hungarian often uses this result-state construction instead:

• Az ajtó be van csukva.

This focuses on the door's condition: it is in a closed state.

So it often corresponds to English is closed, but grammatically it is better thought of as a state/result expression rather than a straightforward passive.

They can both be translated as is closed, but they are not exactly the same.

• be van csukva = shut, physically closed
• be van zárva = closed/locked/closed for access, depending on context

For a door:

• be van csukva means the door is shut
• be van zárva can mean the door is locked, or at least closed off

So in your sentence, be van csukva is a good choice if the important idea is that the door is physically shut while the child sleeps.