Min kone laver kaffe, mens jeg tager jakken på.

Because Danish possessives change according to the gender and number of the noun they belong to.

• min is used with a common gender singular noun
• mit is used with a neuter singular noun
• mine is used with plural nouns

kone is a common gender singular noun, so it takes min:

• min kone = my wife

Compare:

• mit hus = my house
• mine børn = my children

In this sentence, yes: min kone means my wife.

The word kone can also appear in other meanings in Danish, such as woman or old woman in certain contexts, but those uses can sound old-fashioned, rough, or rude depending on the situation. For a learner, the safest and most important meaning here is simply wife.

Because lave is the natural verb for make or prepare in this context.

So:

• lave kaffe = make coffee

Although English uses make, Danish does not always use one single verb the way English does. Here, gøre would not sound natural.

You may also hear:

• brygge kaffe = brew coffee

That focuses more specifically on the brewing process. But lave kaffe is very common and natural everyday Danish.

Because kaffe is being used as an uncountable noun, like coffee in English.

When Danish talks about a substance or an unspecified amount, it often uses no article:

• laver kaffe = making coffee

If you say en kaffe, that usually means a coffee, for example one cup or one order of coffee.

So:

• laver kaffe = makes coffee / is making coffee
• bestiller en kaffe = orders a coffee

Mens means while.

It connects two actions that happen at the same time:

• Min kone laver kaffe
• mens jeg tager jakken på

So the whole idea is that one action happens while the other is happening.

Mens introduces a subordinate clause. A very similar word is imens, which also means while.

Because Danish changes word order depending on whether a clause is a main clause or a subordinate clause.

In a main clause, Danish normally uses the verb-second pattern:

• Min kone laver kaffe

Here, the finite verb laver comes in the second position.

But after a subordinating word like mens, the clause is subordinate, and the normal order is:

• subject + verb

So:

• mens jeg tager jakken på

not:

• mens tager jeg jakken på

That is one of the most important word-order patterns in Danish.

Because tage ... på is a very common Danish expression meaning put on when talking about clothes.

It works like a verb + particle expression. With a noun object, Danish usually places the object between the verb and the particle:

• tage jakken på
• tage skoene på
• tage en hat på

So på comes after the object.

With a pronoun, you also get:

• tage den på = put it on

Because Danish usually shows definiteness by adding an ending to the noun.

Compare:

• en jakke = a jacket
• jakken = the jacket

So instead of using a separate word like English the, Danish often adds -en, -et, or another definite ending to the noun itself.

In this sentence, jakken refers to a specific jacket, probably the speaker’s own jacket or one that is already understood from the situation.

Yes. It is the standard everyday way to say that.

Danish often uses tage ... på for putting on clothes and accessories:

• tage jakken på = put on the jacket
• tage sko på = put on shoes
• tage briller på = put on glasses

A useful contrast is:

• tage jakken på = put the jacket on
• have jakken på = have the jacket on / be wearing the jacket

So tage describes the action, while have describes the resulting state.

Because Danish usually uses the ordinary present tense for actions happening now.

So:

• laver can mean makes or is making
• tager can mean takes or, in context, is putting on

Danish does have ways to stress that something is in progress, but in everyday language the simple present is very often enough. In this sentence, the word mens already makes it clear that the two actions are happening at the same time.

Because mens jeg tager jakken på is a subordinate clause, and many Danish writers put a comma before subordinate clauses.

So the comma helps show the sentence structure:

• main clause: Min kone laver kaffe
• subordinate clause: mens jeg tager jakken på

You may also see Danish written without this comma, because Danish has more than one accepted comma system. But the comma here is completely normal and very common.