Optikeren forklarer nærsynetheden.

Because Danish usually puts the definite article at the end of the noun.

• en optiker = an optician
• optikeren = the optician

So -en here is the definite ending for a singular common-gender noun.

Nærsynethed means nearsightedness / myopia.
Nærsynetheden means the nearsightedness.

Again, Danish marks definiteness by adding an ending:

• nærsynethed = nearsightedness
• nærsynetheden = the nearsightedness

To an English speaker, the nearsightedness may sound a bit more specific than English normally uses, but Danish often uses the definite form where English would simply use the bare abstract noun.

Forklarer is the present tense of at forklare = to explain.

So:

• at forklare = to explain
• forklarer = explains / is explaining

Danish present tense is very simple: the verb does not change depending on the subject.

• jeg forklarer = I explain
• du forklarer = you explain
• optikeren forklarer = the optician explains

Because in Danish, the definite article is usually attached to the noun instead of standing before it.

In this sentence:

• optiker-en = the optician
• nærsynethed-en = the nearsightedness

This is one of the biggest structural differences from English.

The sentence has normal subject–verb–object order:

• Optikeren = subject
• forklarer = verb
• nærsynetheden = object

So literally the structure is:

The optician + explains + the nearsightedness

Yes. This sentence is a normal main clause, and Danish follows the verb-second rule in main clauses.

Here, the subject comes first, so the verb naturally comes second:

• Optikeren forklarer nærsynetheden.

But if you move another element to the front, the verb still stays in second position:

• I dag forklarer optikeren nærsynetheden.
  = Today the optician explains the nearsightedness.

Notice that Danish does not keep the English-style order Today the optician explains... by default; the finite verb must stay second.

It is a layered word:

• nærsynet = near-sighted
• -hed = a noun-forming ending, similar to English -ness
• -en = the definite singular ending

So:

• nærsynet = near-sighted
• nærsynethed = near-sightedness
• nærsynetheden = the near-sightedness

This kind of word-building is very common in Danish.

The hardest parts for English speakers are usually æ and y.

• æ is somewhat like the vowel in cat, but not exactly the same.
• y has no true English equivalent. A useful trick is to say ee while rounding your lips.

So in nærsynetheden, the y sound is especially worth practicing.

You do not need a perfect accent right away, but recognizing that y is its own vowel in Danish is important.

Usually, yes in everyday language, though the exact job title can overlap a bit with English categories.

In Danish, optiker is the person who works with glasses, eyesight testing, and related services in an optics shop. Depending on context, English might translate it as optician or sometimes optometrist.

If you specifically mean an eye doctor, Danish would more likely use øjenlæge.

Yes, it is grammatical and understandable. It sounds a bit formal or textbook-like, which is normal for learning examples.

In real life, Danish speakers might also say things like:

• Optikeren forklarer, hvad nærsynethed er.
  = The optician explains what nearsightedness is.

But the original sentence is still a perfectly useful model for learning noun endings and basic word order.