Min mor synger stille, før babyen falder i søvn.

Because mor is a common-gender noun in Danish. Danish possessives agree with the noun:

• min for common gender
• mit for neuter
• mine for plural

So:

• min mor = my mother
• mit barn = my child
• mine børn = my children

When you use a possessive like min, Danish normally does not use an article as well. So min mor works like English my mother, not the my mother.

This is the normal pattern:

• min mor
• din far
• hendes baby

The -en is the definite article attached to the noun. In Danish, definiteness is often shown as an ending instead of a separate word.

So:

• en baby = a baby
• babyen = the baby

That is why the sentence has babyen rather than a separate word for the.

They are both in the present tense. In Danish, the present tense is usually formed by adding -r to the verb’s infinitive:

• at synge → synger
• at falde → falder

In this sentence, Danish uses the present tense in the same kind of way English does:

• mor synger = mother sings / is singing
• babyen falder i søvn = the baby falls asleep / is falling asleep

The present tense in Danish can often cover both simple present and present progressive meanings from English.

Here stille means quietly or softly.

Danish does not usually make adverbs with a separate ending like English -ly. Very often the same form is used naturally in context. So where English says quiet → quietly, Danish can simply use stille.

In this sentence:

• synger stille = sings quietly / softly

Here før means before and introduces a subordinate clause:

• før babyen falder i søvn = before the baby falls asleep

So før is working as a conjunction here, not just as an adverb.

Compare:

• før hun kommer = before she comes
• før vi går = before we leave

Because after før, you have a subordinate clause, and Danish subordinate clauses normally keep the subject before the finite verb:

• babyen falder = the baby falls

Main clauses in Danish often show V2 word order, where the finite verb comes early in the sentence, but subordinate clauses do not use that same pattern.

So:

• main clause: Min mor synger stille
• subordinate clause: før babyen falder i søvn

Literally, it is something like falls into sleep. But in normal English, the natural translation is falls asleep.

This is a very common Danish expression:

• at falde i søvn = to fall asleep
• han faldt i søvn = he fell asleep
• babyen falder i søvn = the baby falls asleep

It is best learned as a fixed expression.

That comma marks the beginning of the subordinate clause før babyen falder i søvn.

In Danish, comma use before subordinate clauses depends somewhat on the comma system being followed:

• with traditional/grammatical comma, the comma before før is used
• with new comma, it may be left out in a sentence like this

So both of these may be seen:

• Min mor synger stille, før babyen falder i søvn.
• Min mor synger stille før babyen falder i søvn.

The version with the comma is completely standard.