Láska je důležitá.

Because láska is a feminine singular noun, and the adjective has to agree with it.

• láska = feminine singular
• důležitá = feminine singular form of důležitý = important

So Czech is doing something English does not usually show clearly: the adjective changes form to match the noun.

Other forms would be:

• důležitý = masculine singular
• důležitá = feminine singular
• důležité = neuter singular / some plural uses

In this sentence, důležitá matches láska.

Je is the 3rd person singular present tense of být, which means to be.

So:

• já jsem = I am
• ty jsi = you are
• on / ona / ono je = he / she / it is

In Láska je důležitá, je means is.

Láska is feminine.

A very common clue is the ending -a. Many Czech nouns ending in -a are feminine, though not all nouns follow this perfectly.

So here:

• láska = love
• gender: feminine

That is why the adjective is důležitá, not důležitý.

Yes. It is still an adjective.

In Láska je důležitá, the structure is:

• Láska = subject
• je = verb
• důležitá = adjective describing the subject

This is similar to English Love is important.
The adjective comes after is, but it is still an adjective, not an adverb.

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

So Láska je důležitá can mean something like:

• Love is important
• The love is important only in a very specific context, though this sentence usually sounds general

Czech relies on context much more than English does for this.

Yes, effectively the key forms here are nominative.

• láska is nominative singular because it is the subject.
• důležitá is also in the nominative feminine singular, agreeing with the subject after být.

After to be, Czech often uses an adjective in the nominative:

• Láska je důležitá.
• Dům je velký.
• Práce je těžká.

So this is a very normal pattern.

Yes, Czech word order is flexible, but the emphasis changes.

The neutral version is:

• Láska je důležitá.

You could also say:

• Důležitá je láska.

That sounds more like It is love that is important or Love is what is important.
So the meaning stays close, but the focus changes.

In a normal complete sentence, no. You should say:

• Láska je důležitá.

Leaving out je would sound incomplete in standard Czech, except possibly in:

• poetry
• notes
• headlines
• very informal stylized speech

So for learners, it is best to keep je.

A simple learner-friendly approximation is:

• Láska ≈ LAAS-ka
• je ≈ ye
• důležitá ≈ doo-LEH-zhi-taa

A few key points:

• Czech stress is usually on the first syllable of each word.
• á is a long vowel.
• ů is a long ú-like sound.
• ž sounds like the s in measure.

So:

• LÁS-ka
• je
• DŮ-le-ži-TÁ

Even though the main word stress is normally at the beginning of the word, long vowels still matter and should be held a bit longer.

The accent marks show vowel length.

• á = long a
• ů = long u

So:

• a and á are different in Czech
• u and ů are also different in length

Length matters because it can change pronunciation and sometimes meaning.

In this sentence:

• Láska has long á
• důležitá has long ů and long final á

Because důležitá is the correct feminine singular adjective ending.

The base adjective is:

• masculine: důležitý

From that, the feminine form is:

• důležitá

The long á is part of the grammatical ending, not just pronunciation decoration.

The dictionary form is usually the masculine singular form:

• důležitý

Czech dictionaries normally list adjectives in that form, even if the sentence uses a different one.

So if you want to look up důležitá, search for důležitý.

Yes, most likely.

Without extra context, Láska je důležitá is understood as a general statement: love is important.

So láska here is being used in a broad, abstract sense, not necessarily about one specific romantic relationship.