Я не нарочно опоздал, просто автобус застрял в пробке.

It means not on purpose or not intentionally.

So Я не нарочно опоздал is literally I was late not on purpose. In natural English, that becomes I didn’t mean to be late or I wasn’t late on purpose.

Нарочно by itself means on purpose / deliberately, so adding не reverses that idea.

Опоздал is the past tense of the perfective verb опоздать, and it means ended up being late as a completed fact.

Russian uses the perfective here because the speaker is talking about one finished event:

• Я опоздал = I was late / I ended up late

If you said опаздывал, that would be imperfective and would suggest a process, repetition, or background situation, which is not the main idea here.

Yes. In the past tense, Russian verbs agree in gender and number.

Here:

• опоздал = masculine singular
• опоздала = feminine singular
• опоздали = plural

So this sentence sounds like it is being said by a male speaker. If a woman said it, it would be:

Я не нарочно опоздала, просто автобус застрял в пробке.

Yes, very often.

Russian often drops personal pronouns when the meaning is clear from context and the verb form. So you could also hear:

Не нарочно опоздал, просто автобус застрял в пробке.

That sounds natural in conversation, especially if it is already obvious who is speaking.

Yes, you could say Я опоздал не нарочно. Russian word order is flexible.

The version in your sentence puts не нарочно before опоздал to highlight the speaker’s defense right away:

• I didn’t do it on purpose — I was just late because...

The version Я опоздал не нарочно is also understandable, but it sounds a little less focused on the excuse at the start.

Here просто works like just or it’s just that.

It does not mean simple here. It introduces an explanation:

• Я не нарочно опоздал, просто автобус застрял в пробке.
• I wasn’t late on purpose, it’s just that the bus got stuck in traffic.

This use of просто is very common in spoken Russian.

Because there are two separate clauses:

• Я не нарочно опоздал
• автобус застрял в пробке

The word просто links them, but they are still two parts with their own verbs, so Russian uses a comma here.

Because they are in different grammatical roles and cases.

• автобус is the subject of the second clause, so it is in the nominative case.
• в пробке means in traffic / in a traffic jam, and after в with the meaning of location, Russian uses the prepositional case.

So:

• автобус = the bus
• в пробке = in the traffic jam

The form пробке is the prepositional singular of пробка.

It means got stuck in traffic or was stuck in a traffic jam.

The verb застрять literally means to get stuck. In this sentence it describes the bus as unable to move because of the traffic jam.

This is a very common Russian expression:

• застрять в пробке = to get stuck in traffic

Both are common, but they are not exactly the same.

• попал в пробку = got into a traffic jam
• застрял в пробке = got stuck in a traffic jam

Попал focuses on entering the traffic jam.
Застрял focuses on being unable to move because of it.

In your sentence, застрял is a good choice because it clearly explains why the speaker became late.

You often do, but you do not have to.

If you want to say what you were late for, Russian usually uses на + accusative:

• опоздал на урок = was late for class
• опоздал на встречу = was late for the meeting

In your sentence, that information is simply omitted because it is not important or is already understood from context.

They are close, but not identical.

• не нарочно = not on purpose
• не специально = not intentionally / not deliberately
• случайно = by accident

In many situations they overlap, but не нарочно is especially natural when someone is defending themselves or apologizing:

• Я не нарочно! = I didn’t mean it!

So in this sentence, не нарочно sounds very natural and conversational.