Amíg a fogorvos fúr, én a széken ülök.

Here amíg means while: it introduces a time clause describing something happening at the same time as the main action.

So:

• Amíg a fogorvos fúr = While the dentist is drilling
• én a széken ülök = I am sitting in the chair

A useful thing to know is that amíg can also mean as long as in other contexts, so its exact meaning depends on the sentence.

Hungarian normally separates a subordinate clause from the main clause with a comma.

So the sentence is divided into:

• Amíg a fogorvos fúr = subordinate time clause
• én a széken ülök = main clause

That is why the comma appears after fúr.

A fogorvos means the dentist.

It breaks down as:

• a = the
• fogorvos = dentist

The noun fogorvos is built from:

• fog = tooth
• orvos = doctor

So literally it is something like tooth-doctor.

In both places, a is the definite article, meaning the.

• a fogorvos = the dentist
• a széken = on the chair / in the chair

Hungarian uses the definite article very regularly, often in places where English also uses the.

A small grammar note:

• a is used before most consonants
• az is used before vowels

So you get a fogorvos, but for a vowel-initial noun you would get az orvos.

Fúr is the third person singular present tense form of the verb fúr, meaning to drill.

So:

• fúrok = I drill
• fúrsz = you drill
• fúr = he/she/it drills

In this sentence, a fogorvos fúr means the dentist is drilling or the dentist drills, depending on context. Hungarian present tense often covers what English expresses with both simple present and present continuous.

Yes, the verb already shows the subject.

• ülök already means I sit / I am sitting

So én is not strictly necessary for basic grammar. It is included for emphasis, contrast, or clarity.

Here én can suggest something like:

• While the dentist drills, I sit in the chair
• or slightly more contrastively, While the dentist is drilling, I’m the one sitting in the chair

Without én, the sentence would still be completely natural:

• Amíg a fogorvos fúr, a széken ülök.

Because Hungarian uses case endings instead of prepositions in many situations.

• szék = chair
• széken = on the chair

The ending -n / -on / -en / -ön is the superessive case, often meaning on a surface.

So:

• a széken ülök literally means I sit on the chair

However, in English, with a dentist’s chair, we would often naturally say I’m sitting in the chair, even though Hungarian uses széken.

Hungarian case endings have vowel harmony and also stem-based form choices.

For the superessive case, the possible endings are:

• -on
• -en
• -ön

With szék, the correct form is széken.

This is something learners often need to memorize noun by noun at first. Hungarian does have patterns, but the exact surface form is not always fully predictable just from English-style logic.

So the important form to learn is:

• szék → széken

It can mean either, depending on context.

Hungarian present tense often covers both:

• I sit
• I am sitting

So a széken ülök can be understood as:

• I sit on the chair
• I am sitting in the chair

In this sentence, because it describes an ongoing situation during the dentist’s action, English would most naturally use I am sitting.

Yes, Hungarian word order is flexible, and different orders can shift the emphasis.

The version here is neutral and natural:

• én a széken ülök

But other versions are possible, for example:

• Amíg a fogorvos fúr, a széken ülök.
  Neutral, without emphasizing I

• Amíg a fogorvos fúr, én ülök a széken.
  Slightly more focus on the action sitting

• Amíg a fogorvos fúr, a széken én ülök.
  Strong contrast, something like I’m the one in the chair

So Hungarian word order is not random: moving elements changes what is highlighted.

Yes. Fúr literally means to drill, and it is a normal verb for drilling, including a dentist drilling a tooth.

So a fogorvos fúr is a straightforward and natural way to say the dentist is drilling.

Depending on context, Hungarian might also express the object if needed, for example if you want to say exactly what is being drilled, but it is not necessary here.

Yes, in some contexts amíg can be understood more like until, especially when the idea is up to the point when.

But in this sentence, because both actions are presented as happening at the same time, the natural meaning is while.

So here you should read:

• Amíg a fogorvos fúr... = While the dentist drills / is drilling...

not Until the dentist drills...