Hospodský kvíz je vědomostní soutěž.

Here it is an adjective modifying kvíz.

• hospodský kvíz = pub quiz
• literally, hospodský means something like pub-related or of a pub

Be careful: hospodský can also be a noun in other contexts, meaning pub owner / innkeeper / landlord. But in this sentence, because it stands directly before kvíz, it is clearly an adjective.

Because it agrees with kvíz.

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

• gender
• number
• case

kvíz is:

• masculine
• singular
• nominative

So the adjective also takes the masculine singular nominative form:

• hospodský kvíz

If the noun changed, the adjective would change too.

Yes. It is a borrowed word, originally from English quiz, but it is fully used in Czech.

A few helpful points:

• it is spelled kvíz
• it is treated as a normal Czech noun
• it declines like a masculine inanimate noun

So Czech speakers naturally say things like:

• ten kvíz
• o kvízu
• s kvízem

vědomostní means knowledge-based or testing knowledge.

It comes from:

• vědomost = piece of knowledge / knowledge

So:

• vědomostní soutěž = knowledge competition
• very naturally: quiz competition or knowledge contest

In this sentence, the phrase is giving a definition or classification: a pub quiz is a type of knowledge competition.

Because vědomostní belongs to a type of adjective ending in -í. These adjectives often have the same nominative singular form for masculine, feminine, and neuter.

So you get:

• vědomostní kvíz
• vědomostní soutěž
• vědomostní kolo

The form stays vědomostní in all three.

That does not mean the adjective never changes. It still declines in other cases, but in the nominative singular it looks the same across genders.

Because Czech grammatical gender is not determined only by the final letter.

While many feminine nouns do end in -a, quite a few feminine nouns end in a consonant, especially words like:

• soutěž = competition
• odpověď = answer
• píseň = song
• myš = mouse

So soutěž is simply a feminine noun that happens to end in a consonant.

This is something English speakers often just have to learn word by word.

Both main nouns are in the nominative:

• Hospodský kvíz = nominative
• vědomostní soutěž = nominative

Why? Because this is a sentence with být (to be) that identifies or classifies something:

• X is Y

In Czech, after být, the predicate noun is very often also in the nominative when you are saying what something is.

So this sentence literally has the structure:

• Pub quiz
  • is
    • knowledge competition

je is the 3rd person singular present form of být (to be), so it means is.

• Hospodský kvíz je vědomostní soutěž.
• A pub quiz is a knowledge competition.

In a normal full sentence, you usually do not omit it.

Czech is not like Russian, where the present tense of to be is often dropped. In Czech, je is normally required here.

You might see omission only in special styles such as:

• headlines
• notes
• very compressed definitions

But for ordinary speech and writing, keep je.

Because Czech has no articles.

English says:

• a pub quiz
• the pub quiz

Czech usually just says:

• hospodský kvíz

The listener figures out from context whether the meaning is more like a, the, or just a general statement.

So in this sentence, Czech does not need any separate word corresponding to a before vědomostní soutěž.

Yes, Czech word order is more flexible than English, although the original order is the most neutral here.

Neutral version:

• Hospodský kvíz je vědomostní soutěž.

You could also say:

• Vědomostní soutěž je hospodský kvíz.

But that sounds different in emphasis, almost as if you are defining the second phrase from the first, or focusing on what counts as a pub quiz.

So the original order is the best ordinary choice if you want to say: A pub quiz is a knowledge competition.

A rough English-friendly guide:

• Hospodský ≈ HOS-pod-skee
• kvíz ≈ kveez, but the final z is devoiced, so it sounds closer to kvees
• je ≈ yeh
• vědomostní ≈ VYE-do-most-nee
• soutěž ≈ SOU-tesh (final ž is devoiced, so it sounds like sh)

A few pronunciation points:

• Czech stress is usually on the first syllable of each word.
• í is a long vowel.
• Final voiced consonants are often devoiced, which is why:
  • kvíz sounds like kvís
  • soutěž sounds like souteš

So the whole sentence is approximately:

HOS-pod-skee kvees yeh VYE-do-most-nee SOU-tesh