Læreren giver et enkelt eksempel, så vi bedre forstår ordets betydning.

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

• lærer = teacher
• læreren = the teacher

The ending -en is the definite ending for many common-gender nouns. So læreren literally means teacher-the, but in natural English that is just the teacher.

In Danish, verbs do not change for person the way they do in English.

So:

• jeg giver = I give
• du giver = you give
• han/hun giver = he/she gives
• vi giver = we give

The present tense form is the same for all subjects. Here, giver is the present tense of give.

Because eksempel is a neuter noun in Danish.

Danish singular nouns take either:

• en for common gender
• et for neuter

So:

• et eksempel = an example
• eksemplet = the example

Unfortunately, noun gender often has to be learned with the noun.

Because it agrees with the neuter noun eksempel.

The basic adjective is enkel, but before a singular neuter noun it usually becomes enkelt.

So:

• en enkel forklaring = a simple/single explanation
• et enkelt eksempel = a simple/single example

That -t is a normal agreement ending for many adjectives with et-nouns.

Here it most naturally means single: a single example.

The adjective enkel / enkelt can mean both:

• simple
• single / one

In this sentence, the idea is that the teacher gives one example so that we understand the meaning better. So single fits best, though simple is also possible in some contexts.

Here så means so that or so in the sense of purpose/result.

So:

• Læreren giver et enkelt eksempel, så vi bedre forstår ...
• The teacher gives a single example so that we better understand ...

It is not the så that means then in a sequence like først ... så .... In this sentence, it introduces the reason or purpose.

Because after så meaning so that, Danish often uses subordinate-clause word order.

That means the subject comes first, and adverbial words often come before the verb:

• så vi bedre forstår ...

This is very natural Danish. You may also hear:

• så vi forstår ordets betydning bedre

That version is also possible, but the sentence you were given is perfectly normal and places bedre earlier in the clause.

Ordets is the genitive form of ordet.

Step by step:

• ord = word
• ordet = the word
• ordets = the word’s / of the word

Danish usually makes the genitive by adding -s. So ordets betydning means the word’s meaning or more naturally in English, the meaning of the word.

Because when a noun is determined by a possessive or genitive, the following noun usually stays in the indefinite form.

So Danish says:

• ordets betydning = the meaning of the word
• lærerens bog = the teacher’s book
• min bil = my car

Not:

• ordets betydningen
• lærerens bogen

The genitive already makes the phrase definite, so you do not also add the definite ending to betydning.

Yes. In standard Danish, a comma is normally written before a subordinate clause like this one.

So the comma helps show that the second part:

• så vi bedre forstår ordets betydning

depends on the first part and expresses purpose/result.

It is both grammatical and helpful for reading.