Světový problém je významný.

A word-by-word breakdown is:

• světový = world / global
• problém = problem
• je = is
• významný = significant / important

So the sentence means something like The global problem is significant or A global problem is significant, depending on context.

Because both are adjectives agreeing with problém.

In Czech, adjectives must match the noun they describe in:

• gender
• number
• case

Here, problém is:

• masculine
• singular
• nominative

So both adjectives take the masculine singular nominative ending -ý:

• světový problém
• problém je významný

This is very normal in Czech.

In Czech, nouns have grammatical gender. Problém is a masculine inanimate noun.

A very common clue is that many masculine nouns end in a consonant, and problém does:

• problém
• dům
• strom

So learners usually memorize problém as a masculine noun from the start.

They are in the nominative.

• světový problém is the subject
• after je (is), the adjective významný also stays in the nominative because it describes the subject

So this is a basic X is Y sentence structure:

• Problém je významný.
• Dům je velký.
• Student je unavený.

Yes, in standard Czech, you normally use je in this kind of sentence.

Czech says:

• Problém je významný. = The problem is significant.

You usually cannot just say:

• Problém významný. ❌

That would sound incomplete in normal standard Czech.

Czech does not use articles like English the and a/an.

So světový problém can mean:

• a global problem
• the global problem

The exact meaning depends on context.

This is something English speakers often have to get used to: Czech leaves that information unstated unless the context makes it clear.

Yes. Czech word order is more flexible than English word order.

The neutral order here is:

• Světový problém je významný.

But you could also hear:

• Významný je světový problém.
• Je významný světový problém? (question)

Changing the order usually changes emphasis or style, not the core meaning.

For a learner, the given version is the safest neutral one.

A rough pronunciation guide is:

• svě-to-vý

Important points:

• ě often makes the previous consonant sound softer or adds a y/j-like glide
• svě sounds roughly like svye
• the stress in Czech is usually on the first syllable

So:

• SVĚ-to-vý

The long ý at the end is a long vowel.

A rough pronunciation is:

• VÝ-znam-ný

Important things:

• stress is on the first syllable
• both ý vowels are long
• the middle part znam sounds about like znam

So even though Czech marks vowel length, the word stress still stays on the first syllable.

They mostly show vowel length.

For example:

• ý = a long i/y sound
• é = a long e sound

So in:

• světový
• problém
• významný

the marked vowels are pronounced longer than short vowels.

Also, ě is special: it is not just a long vowel marker. It affects the pronunciation of the consonant before it.

They are similar, but not always identical.

• důležitý = important
• významný = significant / important / notable

In many contexts, both could work. But významný can sometimes sound a bit more like:

• significant
• meaningful
• notable

So Světový problém je významný sounds a little more formal or abstract than:

• Světový problém je důležitý.

Yes, often you could.

• světový problém = world/global problem
• globální problém = global problem

In many contexts they are close in meaning. But:

• světový is built from svět = world
• globální is a more international/Latinate-style word, similar to English global

Both are natural Czech, but they may feel slightly different in tone depending on context.

No, it is a loanword, ultimately related to the same source as English problem.

That is why it looks familiar to English speakers:

• English: problem
• Czech: problém

Czech often adapts such words to its own spelling and pronunciation, which is why the Czech form has é.

The pattern is:

• [adjective + noun] + je + [adjective]

More generally:

• Subject + to be + description

So:

• Světový problém = the subject
• je = linking verb
• významný = predicate adjective

Very similar examples are:

• Ten dům je velký. = That house is big.
• Student je chytrý. = The student is smart.
• Úkol je těžký. = The task is difficult.

This is one of the most useful basic Czech sentence patterns to learn early.