Выступление музыканта на сцене было захватывающим.

Because музыканта is in the genitive case.

Here выступление музыканта means the musician’s performance or more literally the performance of the musician.

• музыкант = musician
• музыканта = of the musician

This is a very common Russian pattern:

• книга студента = the student’s book
• голос певца = the singer’s voice
• выступление музыканта = the musician’s performance

So Russian often uses the genitive where English uses ’s.

Because на сцене shows location, not motion.

• на сцене = on the stage / on stage, where something is happening
• на сцену = onto the stage, showing movement toward it

In this sentence, the performance is taking place on the stage, so Russian uses:

• на
  • prepositional case → на сцене

Compare:

• Музыкант выступал на сцене. = The musician was performing on stage.
• Музыкант вышел на сцену. = The musician went out onto the stage.

Because the subject, выступление, is neuter singular.

Russian past-tense forms agree with the subject in gender and number:

• был = masculine
• была = feminine
• было = neuter
• были = plural

Since выступление is a neuter noun, the sentence needs:

• Выступление ... было ...

So было agrees with выступление, not with музыканта.

Because it is being used as a predicate adjective after было, and in this kind of sentence Russian commonly uses the instrumental case.

So:

• захватывающий = captivating / thrilling
• захватывающим = instrumental singular form

The pattern is very common:

• Фильм был интересным. = The film was interesting.
• Урок был полезным. = The lesson was useful.
• Выступление было захватывающим. = The performance was captivating.

This is one of the things that often feels strange to English speakers, because English does not change the adjective here, but Russian often does.

In standard Russian, было захватывающим is the natural choice here.

Using the full adjective in the nominative, as in было захватывающее, sounds unnatural in this sentence.

A good rule for learners is:

• after past-tense быть with a full adjective, use the instrumental
• so: было захватывающим, был интересным, была полезной? Actually with full adjective after была, it would be полезной in the instrumental feminine

Examples:

• Книга была скучной.
• Путешествие было долгим.
• Выступление было захватывающим.

Выступление means a performance, appearance, speech, or presentation, depending on context.

In this sentence, because we have музыканта and на сцене, it clearly means a musical performance or stage performance.

So it is not just any kind of speaking. The surrounding words tell you what kind of выступление it is.

For example:

• выступление президента = the president’s speech/address
• выступление спортсмена = the athlete’s performance
• выступление музыканта = the musician’s performance

Yes. It comes from захватывать, which literally can mean something like to seize, to grab, or to take hold of.

From that literal idea, it also developed the figurative meaning:

• захватывающий = gripping, exciting, captivating

So when something is захватывающее or захватывающим, it is something that grabs your attention.

That figurative idea is very similar to English words like gripping or captivating.

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

The neutral word order here is:

• Выступление музыканта на сцене было захватывающим.

But other orders are possible for emphasis, for example:

• На сцене выступление музыканта было захватывающим.
• Захватывающим было выступление музыканта на сцене.

These alternatives may sound more literary, emphatic, or context-dependent. For most learners, the original order is the safest and most natural.

Because Russian has no articles.

English says:

• the musician
• the stage
• the performance

Russian usually leaves that meaning to context:

• музыканта
• на сцене
• выступление

So Russian does not have direct equivalents of a and the. You understand whether something is definite or indefinite from the situation, the context, and sometimes word order.

It sounds neutral to slightly formal, and perfectly natural in writing.

A native speaker might also say simpler, more conversational things like:

• Выступление музыканта на сцене было очень интересным.
• Музыкант на сцене выступил потрясающе.
• Его выступление было захватывающим.

But the original sentence is grammatically normal and natural, especially in description, reviews, or written narration.

The sentence breaks down like this:

• Выступление = subject, performance
• музыканта = genitive modifier, of the musician
• на сцене = prepositional phrase, on stage
• было = past-tense linking verb, was
• захватывающим = predicate adjective in the instrumental, captivating

So the structure is roughly:

[Subject] + [modifier] + [location] + [was] + [predicate adjective]

Or more literally:

The performance of the musician on the stage was captivating.

In more natural English: The musician’s performance on stage was captivating.