Min niece binder en blå sløjfe om pakken, fordi hun synes, at en sløjfe gør alt pænere.

Because niece is a common-gender singular noun in Danish.

• min = my, used with common-gender singular nouns
• mit = my, used with neuter singular nouns
• mine = my, used with plural nouns

So:

• min niece = my niece
• mit barn = my child
• mine børn = my children

Yes. Niece is the normal Danish word for niece.

Even though it is spelled the same as in English, the pronunciation is different in Danish. A learner may notice that many family words are close to English or other Germanic languages, but they still follow Danish pronunciation and grammar.

Binder is the present tense of binde.

• at binde = to tie
• binder = ties / is tying

So Min niece binder en blå sløjfe om pakken means:

• My niece ties a blue bow around the package
• or in natural English, My niece is tying a blue bow around the package

Danish present tense often covers both English simple present and present progressive.

This is the normal Danish order:

• en = indefinite article
• blå = adjective
• sløjfe = noun

So:

• en blå sløjfe = a blue bow

The order is the same as in English: article + adjective + noun.

Also note that blå stays the same here because the noun is singular and indefinite.

Because pakken means the package, while en pakke means a package.

Danish often marks definiteness by adding an ending to the noun:

• en pakke = a package
• pakken = the package

So the sentence is talking about a specific package, not just any package.

Here om pakken means around the package.

With binde, Danish often uses om when something is tied around something else:

• binde en sløjfe om pakken = tie a bow around the package

This is a normal idiomatic combination. In English, you might also say on the package, but Danish uses om because the ribbon or bow is understood as going around it.

Synes here means thinks, feels, or finds in the sense of a personal opinion.

• hun synes, at ... = she thinks that ...
• jeg synes, at det er flot = I think it is pretty

This is different from some other Danish verbs:

• tro = believe / think something is true
• mene = mean / hold an opinion, often a bit more deliberate
• synes = think / feel / find, often more personal or subjective

In this sentence, synes fits well because it is about taste and appearance.

Because at introduces a content clause, like English that:

• hun synes, at en sløjfe gør alt pænere
• she thinks that a bow makes everything prettier

In everyday speech, Danish speakers sometimes leave out at, especially in informal language, but including it is very normal and standard in writing.

So this sentence is completely natural and correct with at.

Because both parts after fordi and at are subordinate clauses.

In Danish:

• Main clauses normally follow verb-second word order.
• Subordinate clauses usually have subject before verb.

So:

• Main clause: Min niece binder ...
• Subordinate clause after fordi: hun synes ...
• Subordinate clause after at: en sløjfe gør alt pænere

That is why you get:

• fordi hun synes
• not fordi synes hun

and

• at en sløjfe gør alt pænere
• not at gør en sløjfe alt pænere

Gør means makes, and pænere is the comparative form of pæn.

• pæn = pretty / nice / neat
• pænere = prettier / nicer

So:

• en sløjfe gør alt pænere = a bow makes everything prettier

This is a very common Danish pattern:

• gøre noget bedre = make something better
• gøre noget nemmere = make something easier
• gøre noget smukkere = make something more beautiful

Because after gøre, Danish often uses a comparative adjective directly:

• gøre alt pænere = make everything prettier

That is usually more natural than gøre alt mere pænt in this kind of sentence.

Also note:

• alt = everything
• pænere describes the result: everything becomes prettier

So the structure is very similar to:

• Det gør huset større = It makes the house bigger
• Det gør maden bedre = It makes the food better

Because en sløjfe in the second clause is not just referring to the exact same bow as a physical object. It is expressing a general idea:

• a bow makes everything prettier

That is more like a general statement about bows in general. If you used den, it would sound more like you were talking only about that one specific bow.

So:

• en sløjfe gør alt pænere = a bow makes everything prettier
• den gør alt pænere = it makes everything prettier

Both are possible in some contexts, but the version with en sløjfe sounds more general and natural here.

Because Danish writing often marks subordinate clauses with commas.

Here:

• ..., fordi hun synes, ...
• ..., at en sløjfe gør ...

So the commas help show the structure of the sentence.

This is especially useful in longer Danish sentences, where clause boundaries matter a lot. Even if spoken Danish would not pause much, the commas are standard in writing.