Indboforsikringen dækker indboet.

Because Danish, like German, very often makes compound nouns by joining words together.

Here, indboforsikring is built from:

• indbo = household contents
• forsikring = insurance

So indboforsikring means contents insurance / household contents insurance.

Then the definite ending -en is added:

• indboforsikring = contents insurance
• indboforsikringen = the contents insurance / the contents insurance policy

So the whole word is not unusual in Danish at all.

The ending -en is the definite article attached to the noun.

In Danish, instead of usually putting a separate word like the before the noun, you often add the definite ending directly to the noun:

• en forsikring = an insurance policy
• forsikringen = the insurance policy

Since indboforsikring is a common-gender noun, its definite singular form takes -en:

• indboforsikring → indboforsikringen

So indboforsikringen means the contents insurance.

Because in Danish, the definite article is usually a suffix, not a separate word.

So:

• English: the insurance
• Danish: forsikringen

And:

• English: the contents
• Danish: indboet

This is the normal pattern when there is no adjective in front of the noun.
If there were an adjective, Danish would usually use both a separate definite word and a definite ending, for example:

• det store hus = the big house

But in your sentence, the nouns stand alone, so the attached endings are enough.

Because indbo is a neuter noun.

Danish singular nouns have two grammatical genders:

• common gender
• neuter

The definite singular endings are usually:

• common gender: -en
• neuter: -et

So:

• et indbo = household contents
• indboet = the household contents

That is why the object ends in -et, not -en.

Dækker is the present tense of the verb at dække.

So:

• at dække = to cover
• dækker = covers / is covering

In this sentence, it means covers in a general, factual sense:

• Indboforsikringen dækker indboet.
• The contents insurance covers the contents.

Danish present tense is often formed by adding -r to the infinitive:

• at købe → køber
• at betale → betaler
• at dække → dækker

No, this sentence has the basic subject–verb–object order:

• Indboforsikringen = subject
• dækker = verb
• indboet = object

So it follows a very familiar pattern for an English speaker:

• The insurance covers the contents.

Danish does have a strong verb-second rule, but in a simple main clause like this, that gives the same order you would expect:

• subject first
• finite verb second

The base, or indefinite singular, forms are:

• en indboforsikring
• et indbo

Then the definite forms used in the sentence are:

• indboforsikringen
• indboet

So you can think of the sentence as using:

• the contents insurance
• the household contents

This is useful because dictionary entries normally give the base forms, not the definite ones.

It is usually understood as a collective noun.

Indbo refers to the household contents as a whole: furniture, belongings, and other items in a home. So even though English might use a plural idea like contents or belongings, Danish often uses the singular noun indbo.

That is why indboet here does not mean just one single item. It means the contents collectively.

A rough pronunciation guide for an English speaker is:

IN-bo-for-SIK-ring-en DEK-er IN-bo-eth

A few points:

• dækker has an æ sound, somewhat like the vowel in cat, but not exactly the same.
• The d in dækker is a normal d sound.
• The d in indboet is not strongly pronounced the way English speakers might expect.
• The final -et in indboet is usually light, not heavily stressed.

The main stresses are roughly on:

• indboforsikringen: -SIK-
• dækker: first syllable
• indboet: first syllable

Grammatically, you can use the indefinite forms in some contexts, but it would mean something different.

Compare:

• Indboforsikringen dækker indboet.
  = The contents insurance covers the contents.

• En indboforsikring dækker indbo.
  = A contents insurance policy covers household contents.

The sentence you were given sounds like it is talking about a specific policy and specific contents, or making a general statement with definite nouns. Removing the endings changes the meaning, not just the grammar.

Because dækker is a finite verb, not an infinitive.

English uses:

• to cover = infinitive
• covers = present tense

Danish uses:

• at dække = infinitive
• dækker = present tense

In a normal statement, Danish uses the finite verb:

• Indboforsikringen dækker indboet.

So this is exactly parallel to English covers, not to cover.