Эта цитата звучит просто, но в ней скрыта важная загадка.

Because цитата is a feminine noun in Russian. The demonstrative этот changes to match the noun’s gender:

• этот = masculine
• эта = feminine
• это = neuter
• эти = plural

So:

• эта цитата = this quote

A native English speaker often has to get used to the fact that Russian words like this must agree with the noun.

In Russian, звучать can be used both literally and figuratively, much like English to sound.

So:

• это звучит странно = that sounds strange
• цитата звучит просто = the quote sounds simple

Even though a quote is written text, Russian still uses звучит naturally to talk about the impression it gives.

Because просто is an adverb, and it describes how it sounds.

Compare:

• простая цитата = a simple quote
  
  • here простая describes the noun цитата
• цитата звучит просто = the quote sounds simple
  
  • here просто describes the verb звучит

This is very similar to English:

• a simple quote
• the quote sounds simple

After verbs like звучать, Russian usually uses an adverb.

Но means but. It connects two contrasting ideas:

• Эта цитата звучит просто = This quote sounds simple
• но в ней скрыта важная загадка = but an important mystery is hidden in it

The contrast is:

• outwardly simple
• inwardly deep or puzzling

So но marks that change in perspective.

В ней means in it and uses the prepositional case.

The pronoun comes from она because it refers back to цитата, which is feminine.

Forms of она include:

• она = she / it
• её / её = her
• ей = to her
• ею / ей = by/with her
• о ней / в ней = about her / in her

So:

• в ней = in it

Russian uses the same feminine pronoun form whether English would say she or it.

Скрыта is the short form of скрытый / скрытая / скрытое / скрытые, and here it means hidden in a predicative sense: is hidden.

So:

• скрытая загадка = a hidden mystery
  
  • full form, used before a noun
• загадка скрыта = the mystery is hidden
  
  • short form, used as part of the predicate

In this sentence:

• в ней скрыта важная загадка = an important mystery is hidden in it

Why not скрывается?

• скрывается means is hiding itself, is concealed, or is being hidden depending on context
• скрыта is a more compact and literary way to say is hidden

So скрыта sounds very natural and elegant here.

Because важная загадка is the grammatical subject of the second clause.

The structure is basically:

• в ней = in it
• скрыта = is hidden
• важная загадка = an important mystery

Even though English often starts with the subject, Russian can place the location first:

• В ней скрыта важная загадка

This word order is normal in Russian. The noun загадка stays in the nominative case because it is the thing that is hidden.

It can mean both, depending on context.

Common meanings of загадка include:

• riddle
• puzzle
• mystery
• something hard to understand

In this sentence, mystery is usually the best choice, because the idea is not necessarily a literal riddle with an answer, but something deeper hidden inside the quote.

So важная загадка suggests:

• an important mystery
• an important puzzle
• something significant that needs to be understood

Russian word order is flexible, and different orders change the emphasis.

• В ней скрыта важная загадка puts emphasis first on where the mystery is hidden: in it
• Важная загадка скрыта в ней puts emphasis first on what is hidden: an important mystery

The version in your sentence sounds natural and slightly more literary. It guides the reader like this:

1. the quote seems simple
2. but inside it
3. there is something important hidden

So the chosen word order helps create a more dramatic effect.

It is best understood here as a short-form passive participle/adjectival form used as part of the predicate.

For learners, the easiest practical way to think about it is:

• скрытая = hidden, when directly modifying a noun
• скрыта = is hidden

Examples:

• скрытая мысль = a hidden thought
• мысль скрыта = the thought is hidden

So in this sentence, скрыта functions like the is hidden part of the clause.

Yes, grammatically you could, but it would not mean exactly the same thing.

Compare:

• в ней есть важная загадка = there is an important mystery in it
• в ней скрыта важная загадка = an important mystery is hidden in it

The second version is stronger and more expressive. Скрыта suggests that the mystery is not obvious; it is concealed beneath the surface. That matches the first clause звучит просто very well.

So есть is possible, but скрыта is much better stylistically here.