Provozní řád a odpovědnost jsou důležité.

Because the subject is plural.

The sentence has two things joined by a (and):

• provozní řád
• odpovědnost

So Czech treats them together as a plural subject, and the verb být (to be) must also be plural:

• je = is
• jsou = are

So:

• Provozní řád je důležitý. = The operating rules are important. / The rulebook is important.
• Odpovědnost je důležitá. = Responsibility is important.
• Provozní řád a odpovědnost jsou důležité. = The operating rules and responsibility are important.

Because it agrees with a plural subject.

In Czech, adjectives used after to be still agree with the subject in number and gender.

Here the subject is made of:

• řád = masculine inanimate singular
• odpovědnost = feminine singular

Together they form a plural subject. Since there is no masculine animate noun in the group, Czech uses the non-masculine-animate plural agreement, which here gives:

• důležité

That is why you get:

• jsou důležité

and not:

• je důležitý
• je důležitá

They are in the nominative case, because they are the subject of the sentence.

You can tell because they are the things that are important.

• provozní řád = nominative singular
• odpovědnost = nominative singular

Even though each noun is singular by itself, together they make a plural subject, which is why the verb is jsou.

Provozní řád is a set phrase. It often means something like:

• operating rules
• rules of operation
• house rules
• regulations for how a place/facility/service is run

The exact English translation depends on context.

For example, in different situations it could refer to rules for:

• a school
• a swimming pool
• a workplace
• a building
• a public facility

So a learner should understand it as a practical or official set of rules governing operation.

Provozní is an adjective related to provoz, which means:

• operation
• running
• traffic/activity of a business or facility

So provozní means something like:

• operational
• relating to operation/running

In provozní řád, it describes the type of řád: not just any order/rulebook, but one connected with how something operates.

Not quite in the everyday English sense of order.

The Czech word řád has several meanings depending on context, such as:

• order
• system
• code
• regulations
• rulebook

In the phrase provozní řád, it usually means a formal set of rules or regulations, not simply orderliness.

So translating it word-for-word as operational order would sound unnatural in English. A more natural translation is usually:

• operating rules
• operating regulations
• house rules

Because Czech has no articles.

English uses:

• a / an
• the

Czech does not have direct equivalents in normal grammar. So:

• Provozní řád a odpovědnost jsou důležité.

can mean, depending on context:

• The operating rules and responsibility are important
• Operating rules and responsibility are important

Context tells you whether the meaning is definite or more general.

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

The basic neutral version is:

• Provozní řád a odpovědnost jsou důležité.

But you could also say:

• Důležité jsou provozní řád a odpovědnost.

This puts more emphasis on důležité (important), as if answering the question What is important?

So the meaning stays very similar, but the emphasis changes.

In this sentence, a is the normal word for and.

• a = and

Czech also has i, which can sometimes mean and, but it often has an added sense like:

• also
• even
• as well as

So for a simple joining of two nouns, a is the most natural choice:

• provozní řád a odpovědnost

Using i here would sound different and would usually need a special context or emphasis.

It is singular.

• odpovědnost = responsibility

Even though English sometimes uses abstract nouns in slightly different ways, here Czech is using the singular abstract noun.

But remember: the whole subject is still plural because it is:

• provozní řád
  • odpovědnost

joined by a.

So:

• odpovědnost = singular noun
• whole subject = plural
• verb = jsou

The verb and adjective would change to match each noun.

With provozní řád alone:

• Provozní řád je důležitý.

Why?

• řád is masculine inanimate singular
• so the adjective is důležitý

With odpovědnost alone:

• Odpovědnost je důležitá.

Why?

• odpovědnost is feminine singular
• so the adjective is důležitá

With both together:

• Provozní řád a odpovědnost jsou důležité.

So this is a good example of Czech agreement changing according to gender and number.

It could be either, depending on context.

Because Czech has no articles, the sentence itself does not tell you as clearly as English whether it means:

• the operating rules and responsibility are important or
• operating rules and responsibility are important

In real use, context would decide. For example:

• in a workplace, it may refer to a specific official provozní řád
• in a general statement, it may mean the idea of operating rules and responsibility more broadly

So the grammar allows both, and context supplies the exact interpretation.