Kærligheden er ægte.

Because Danish usually puts the definite article on the end of the noun instead of using a separate word.

• kærlighed = love
• kærligheden = the love

So where English says the love, Danish often says it as one word.

The dictionary form is kærlighed.

Its forms are:

• en kærlighed = a love
• kærligheden = the love

So the noun is common gender and takes -en in the definite singular.

Er is the present tense of at være, which means to be.

So:

• er = is

This works just like English in a sentence such as The love is genuine.

Yes. This is the standard order for a simple statement:

• Kærligheden = subject
• er = verb
• ægte = complement/adjective

So the structure is basically:

Subject + verb + adjective

Also, Danish main clauses usually put the finite verb in the second position. Here the subject comes first, so er naturally comes second.

Many Danish adjectives change depending on gender, number, or definiteness, but ægte is one of the adjectives that usually stays the same.

For example:

• en ægte følelse = a genuine feeling
• et ægte smil = a genuine smile
• ægte følelser = genuine feelings

So in Kærligheden er ægte, the form ægte is correct as it is.

Usually kærligheden refers to a specific love, not the general idea of love.

So it often means something like:

• the love between two people already being talked about
• this love in a particular situation

If you wanted to talk about love more generally, Danish would more often use kærlighed without the definite ending, or a different phrasing depending on context.

Here ægte means genuine, real, or authentic.

With something emotional like love, it suggests that the love is:

• sincere
• not fake
• deep and real

Depending on context, English might translate it as genuine, real, or even true.

A rough learner-friendly guide is:

• kærligheden: the first vowel æ is somewhat like the vowel in cat, but Danish pronunciation is trickier and more rounded/smoother
• er: often sounds like a short, reduced air
• ægte: starts with the same æ sound, and the final -e is a weak uh sound

A very approximate English-style guide could be:

KAIR-li-heh-den air EK-tuh

But that is only approximate. The hardest parts for English speakers are usually:

• the Danish æ
• the soft pronunciation in kærligheden
• the reduced unstressed endings

Sometimes, yes, but not always.

Ægte most literally means genuine or authentic. In some contexts, English naturally says true, especially with feelings or love. But ægte does not always mean exactly the same thing as true in every situation.

So for this sentence:

• The love is genuine is very close
• The love is real also works
• The love is true can work, but it depends more on style and context