Из-за пробки нам пришлось отложить совещание до вечера.

Из-за means because of or due to.

It requires the genitive case, so пробка becomes пробки.

• пробка = traffic jam / cork / stopper
• из-за пробки = because of the traffic jam

This is a very common pattern:

• из-за дождя = because of the rain
• из-за аварии = because of the accident
• из-за пробки = because of the traffic jam

So the case is not random: it is controlled by the preposition из-за.

Yes — пробка has more than one meaning.

Common meanings include:

• cork / bottle stopper
• traffic jam

In this sentence, the context clearly makes it traffic jam.

Examples:

• вынуть пробку из бутылки = to remove the cork from the bottle
• стоять в пробке = to be stuck in traffic

Russian often uses the same word for different meanings, just like English does.

Because пришлось comes from прийтись / приходиться, which is often used in an impersonal construction.

In this pattern, the person who is affected is put in the dative case:

• мне пришлось = I had to
• тебе пришлось = you had to
• нам пришлось = we had to

So:

• нам = to us
• пришлось = it was necessary / it fell to us / we had to

Literal-ish sense:

• Нам пришлось отложить совещание = It turned out that we had to postpone the meeting

You do not say мы пришлось.

Пришлось is the past tense form of прийтись in an impersonal use. In everyday English, it usually means:

• had to
• was forced to
• ended up having to

So in this sentence:

• нам пришлось отложить совещание = we had to postpone the meeting

It often suggests that the action was necessary because of circumstances, not because someone wanted to do it.

Compare:

• Мы отложили совещание = We postponed the meeting.
• Нам пришлось отложить совещание = We had to postpone the meeting.

The second one adds the idea of necessity.

Because this is an impersonal sentence.

In Russian, impersonal predicates are often put in the neuter singular past form:

• мне пришлось
• нам удалось
• ему повезло
• ей стало плохо

There is no normal grammatical subject like мы controlling the verb. The verb stays in the default impersonal form, and the affected person appears in the dative:

• нам пришлось = we had to
• literally more like to us it became necessary

Because отложить is perfective, and here the sentence refers to one completed action: the decision/action to postpone the meeting.

• откладывать = imperfective, to postpone / to be postponing / to postpone repeatedly
• отложить = perfective, to postpone once, to put off

After пришлось, Russian often uses the infinitive that matches the specific situation:

• Нам пришлось отложить совещание. = We had to postpone the meeting.
  One concrete act.

If you used откладывать, it would sound more like an ongoing or repeated process, which does not fit as well here.

Because it is the direct object of отложить.

The verb отложить takes the accusative case:

• отложить что? → совещание

Now, совещание is a neuter inanimate noun, and for neuter inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: совещание
• accusative: совещание

That is why the word does not visibly change.

These all can translate as meeting, but they are not identical.

• совещание = a work meeting, conference, planning meeting, official discussion
• встреча = a meeting/encounter in a broad sense; can be formal or informal
• собрание = an assembly, gathering, meeting of members, often more formal or collective

In this sentence, совещание fits well because it sounds like a work-related or official meeting.

So:

• отложить совещание = postpone the meeting (business/official meeting)

До means until / up to / before, and it requires the genitive case.

So:

• вечер → вечера
• до вечера = until the evening

Examples:

• до утра = until morning
• до понедельника = until Monday
• до конца недели = until the end of the week

So вечера is genitive singular because of до.

Here it means until the evening — in natural English, usually until the evening or to the evening in the sense of moving it later in time.

So the idea is:

• the meeting was supposed to happen earlier
• it was postponed so that it would happen in the evening

If you wanted to emphasize for the evening, Russian might also use other wording depending on context, but до вечера is perfectly natural for postponed until evening.

Do not confuse it with:

• к вечеру = by evening / toward evening
• на вечер = for the evening

Yes. Russian word order is relatively flexible, because case endings show grammatical roles.

The original sentence:

• Из-за пробки нам пришлось отложить совещание до вечера.

This puts the reason first: Because of the traffic jam...

You could also say:

• Нам пришлось отложить совещание до вечера из-за пробки.

This is also correct, but now the reason comes later.

A rough nuance:

• Из-за пробки... = emphasizes the cause from the start
• ...из-за пробки = gives the cause after the main statement

Both are normal.

A more literal breakdown would be:

• Из-за пробки = because of the traffic jam
• нам = to us
• пришлось = it became necessary / we had to
• отложить = to postpone
• совещание = the meeting
• до вечера = until the evening

So a more literal English version would be something like:

Because of the traffic jam, to us it became necessary to postpone the meeting until the evening.

That is not natural English, but it helps show the Russian structure.

The main stresses are:

Из-за́ про́бки нам пришло́сь отложи́ть совеща́ние до ве́чера.

A learner-friendly breakdown:

• из-за́
• про́бки
• нам
• пришло́сь
• отложи́ть
• совеща́ние
• до
• ве́чера

A couple of useful points:

• из-за has stress on the second part: -за́
• пришлось is stressed on the final syllable: пришло́сь
• совещание is stressed on -ща́-: совеща́ние

Not exactly, although both can sometimes translate as had to.

• нам пришлось отложить совещание = we had to postpone the meeting because circumstances forced it
• мы должны были отложить совещание = we were supposed to / were obliged to postpone the meeting

Пришлось usually sounds more like necessity caused by the situation. Должны были sounds more like duty, obligation, or expectation.

In this sentence, because of the traffic jam, пришлось is the more natural choice.