Während er den Hosenbund umnäht, prüfe ich das Knopfloch.

Because während is a subordinating conjunction. In German, a subordinate clause usually sends the conjugated verb to the end.

So:

• Während er den Hosenbund umnäht = While he hems/sews around the waistband

Structure:

• Während = subordinating conjunction
• er = subject
• den Hosenbund = object
• umnäht = verb, placed at the end

This is one of the most important German word-order patterns to learn.

Because the sentence begins with the subordinate clause, and in German the finite verb must still be in second position in the main clause.

So after the full opening clause:

• Während er den Hosenbund umnäht, prüfe ich das Knopfloch.

the main clause starts with the verb prüfe, then the subject ich.

Compare:

• Ich prüfe das Knopfloch, während er den Hosenbund umnäht.
• Während er den Hosenbund umnäht, prüfe ich das Knopfloch.

Both are correct. When the während clause comes first, the main clause has verb first, subject second.

Here, während means while in a time sense: two actions happen at the same time.

So it connects:

• he is sewing around the waistband
• I am checking the buttonhole

It is different from the preposition während meaning during:

• während der Arbeit = during the work

In your sentence, während is a conjunction, not a preposition.

In this sentence, umnähen is being used as an inseparable verb, so it stays together:

• er umnäht
• er hat den Hosenbund umnäht

That is why you do not get:

• er näht den Hosenbund um in this meaning

With sewing vocabulary, umnähen often means something like to sew around, to hem, or to stitch around the edge of something.

This is a good reminder that verbs with prefixes are not always separable just because they look like they could be.

Both are direct objects, so they are in the accusative case.

• umnähen takes a direct object: you sew around something
• prüfen takes a direct object: you check something

So:

• der Hosenbund → den Hosenbund in accusative
• das Knopfloch → das Knopfloch in accusative

Notice that das does not change in the neuter accusative singular.

Hosenbund is a compound noun:

• Hose = trousers / pants
• Bund = band, edge, waistband

Together, der Hosenbund means waistband.

A useful rule for German compounds: the last part determines the gender.

Since der Bund is masculine, the whole word is:

• der Hosenbund

and in the sentence it becomes:

• den Hosenbund (accusative)

Knopfloch is another compound noun:

• Knopf = button
• Loch = hole

So das Knopfloch = buttonhole.

Again, the last part determines the gender:

• das Loch is neuter
• therefore das Knopfloch is also neuter

That is why the sentence has:

• das Knopfloch

German usually uses the simple present (Präsens) for actions happening right now.

So:

• er umnäht can mean he sews around or he is sewing around
• ich prüfe can mean I check or I am checking

German normally does not need a separate progressive form like English is sewing.

Context tells you that the actions are happening now.

Yes. A very natural alternative is:

• Ich prüfe das Knopfloch, während er den Hosenbund umnäht.

This has the same basic meaning.

The difference is mostly in emphasis:

• starting with Während... highlights the time relationship first
• starting with Ich prüfe... highlights the main action first

Both versions are grammatically correct.

Yes. In German, a subordinate clause introduced by a word like während is normally separated by a comma from the main clause.

So:

• Während er den Hosenbund umnäht, prüfe ich das Knopfloch.

That comma is required in standard German spelling.

A helpful way is to divide it into two parts:

1. Subordinate clause

   • Während er den Hosenbund umnäht
   • verb at the end

2. Main clause

   • prüfe ich das Knopfloch
   • finite verb in second position

A good formula is:

• [subordinate clause], [finite verb] [subject] ...

So this sentence follows a very common German pattern:

• While X happens, do I Y

which sounds odd in English, but is normal in German word order.

A rough guide:

• um sounds like oom with a short vowel
• näht has a long ä sound, somewhat like the vowel in British air but tenser and cleaner

Very roughly: oom-nayt
But that spelling is only an approximation.

A few pronunciation notes:

• ä in näht is not the same as English a in cat
• h after the vowel shows that the vowel is long
• final -t is clearly pronounced

If you know IPA, it is approximately [ʊmˈnɛːt].

Yes. That is a very common source of confusion.

Während can be:

1. a conjunction

   • clause
   • während er den Hosenbund umnäht
   • while he is sewing around the waistband

2. a preposition

   • noun phrase
   • während der Arbeit
   • during the work

As a preposition, während usually takes the genitive in formal German, though other patterns can appear in everyday usage.

In your sentence, it is definitely a conjunction, because it is followed by a full clause with a subject and verb: er ... umnäht.