Det sidste digt i bogen er kort, men meget smukt.

Here, det is functioning as the definite article/determiner for a neuter noun phrase.

• et digt = a poem
• det sidste digt = the last poem

So in this sentence, det does not mean it. It is part of the noun phrase det sidste digt.

Because digt is a neuter noun in Danish.

You learn the noun as:

• et digt = a poem

Neuter nouns use det in this kind of definite phrase:

• det sidste digt

If the noun were a common-gender en noun, you would use den instead:

• en historie → den sidste historie

This is a very common Danish pattern.

When a noun is definite without an adjective, Danish usually adds the definite ending to the noun:

• digtet = the poem

But when a definite noun has an adjective before it, Danish normally uses:

• den/det/de
  • adjective + noun

So:

• det sidste digt = the last poem

Not:

• det sidste digtet

In other words, with a preceding adjective, the noun usually appears in its indefinite form.

Because sidste is the form used before a noun.

• det sidste digt = the last poem

By contrast, sidst is usually an adverb, not an adjective before a noun:

• Jeg så ham sidst i går. = I saw him last yesterday / most recently yesterday.

So before digt, you need sidste, not sidst.

They can both relate to last/latest, but they are not the same.

• sidste = last/final in a sequence
• seneste = latest/most recent in time

In a book, det sidste digt means the poem that comes last in the book.

If you said det seneste digt, it would sound more like the most recently written/published poem, depending on context.

i bogen means in the book.

• i = in
• bog = book
• bogen = the book

So i bogen is a prepositional phrase telling you which poem we are talking about: the last poem in the book.

You could also say:

• bogens sidste digt

That also means the book’s last poem / the last poem in the book, but det sidste digt i bogen is very natural and often clearer for learners.

They are adjectives. They are predicate adjectives, meaning they come after er and describe the subject.

The subject is:

• Det sidste digt i bogen

And the adjectives describing it are:

• kort
• smukt

So the structure is:

• [subject] + er + [adjective]

Just like English:

• The poem is short
• The poem is beautiful

Because predicate adjectives in Danish usually agree with a neuter singular noun by taking -t.

Since digt is neuter (et digt), you get:

• smuk → smukt

But some adjectives do not show an obvious extra change in spelling. Kort is simply the correct form here:

• et kort digt
• digtet er kort

So both adjectives agree with digt, but only smuk shows the change very clearly.

Because meget here is an adverb meaning very, and it modifies the adjective smukt.

• meget smukt = very beautiful

The adjective still has to agree with the noun:

• digt is neuter
• so smuk becomes smukt

That is why meget smukt is correct.

megen is different. It is used more like much before certain nouns, not as very before an adjective.

Because Danish often leaves out a repeated verb when it is understood from the first part.

So:

• er kort, men meget smukt

really means:

• er kort, men (er) meget smukt

This is completely normal. English does something similar:

• It is short, but very beautiful.

You do not need to repeat is there either.

Because standard Danish punctuation normally uses a comma before men.

So this is the expected written form:

• ... er kort, men meget smukt.

The comma marks the contrast introduced by men = but.

The basic structure is:

• Det sidste digt i bogen = subject
• er = finite verb
• kort, men meget smukt = subject complement

So the sentence follows a simple main-clause pattern:

• Subject + verb + complement

Danish main clauses also follow the V2 rule, which means the finite verb tends to be in the second position. Here, since the subject comes first, the sentence looks very similar to English word order.

Good comparison:

Common gender singular

• Den sidste historie i bogen er kort, men meget smuk.
• The last story in the book is short, but very beautiful.

Here:

• den because historie is an en noun
• smuk instead of smukt

Plural

• De sidste digte i bogen er korte, men meget smukke.
• The last poems in the book are short, but very beautiful.

Here:

• de for plural
• adjectives usually take -e in the plural: korte, smukke