Из-за пробки нам пришлось перенести встречу на вечер.

Из-за is a fixed preposition written with a hyphen. In this sentence it means because of.

So:

• из-за пробки = because of the traffic jam

It can also have a literal spatial meaning in other contexts, like from behind, but here it clearly means because of.

Because из-за requires the genitive case.

The dictionary form is пробка, but after из-за it becomes:

• пробка → пробки

So:

• из-за пробки = because of a traffic jam

Yes, пробка can mean several things depending on context:

• cork / bottle stopper
• traffic jam
• sometimes plug

In this sentence, из-за пробки clearly means because of the traffic jam, because the rest of the sentence is about having to move a meeting.

Because Russian uses an impersonal construction with прийтись to say to have to.

Here:

• нам is dative
• literally, the structure is something like to us it turned out necessary to...

So:

• нам пришлось перенести встречу = we had to postpone/reschedule the meeting

This is different from English, where we is the subject. In Russian, the person affected by пришлось is usually in the dative.

Пришлось is the past tense of прийтись in an impersonal use.

In this pattern, прийтись + infinitive means:

• to have to
• to be forced to
• to end up having to

So:

• нам пришлось перенести встречу = we had to move the meeting

It is very common in Russian and often sounds a bit like the situation forced the action.

Because it is being used impersonally.

In impersonal constructions, Russian often uses:

• past tense neuter singular form

So even though the meaning is we had to, the verb stays in the impersonal form:

• пришлось

You are not matching it to мы here, because there is no normal nominative subject in the sentence.

Because перенести is perfective, and here the sentence refers to one completed action: the meeting was moved to a new time.

Compare:

• перенести = to move/reschedule once, successfully, as a complete action
• переносить = to be moving, to move repeatedly, or to talk about the process in a more general way

After пришлось, Russian often uses the infinitive that fits the situation. Here the meaning is a single completed rescheduling, so перенести is the natural choice.

Встречу is accusative singular.

The dictionary form is:

• встреча = meeting

As the direct object of перенести, it goes into the accusative:

• перенести что? → встречу

So:

• перенести встречу = to move/reschedule the meeting

На вечер means to the evening or for the evening.

It shows the new scheduled time of the meeting.

So:

• перенести встречу на вечер = to move the meeting to the evening

The preposition на with the accusative is often used when something is arranged, postponed, or rescheduled to a particular time.

This is a very common question.

• на вечер = for the evening / to the evening
  This focuses on the new scheduled slot
• вечером = in the evening
  This usually tells you when something happens

So in this sentence:

• перенести встречу на вечер = reschedule the meeting for the evening

If you said перенести встречу вечером, that would more naturally sound like to move the meeting in the evening — that is, the action of moving it happens in the evening, which is not the intended meaning here.

Russian word order is flexible, and the beginning of the sentence often gives the reason, context, or what the speaker wants to emphasize.

So:

• Из-за пробки нам пришлось перенести встречу на вечер.

puts the cause first: Because of the traffic jam...

Other word orders are possible, for example:

• Нам пришлось перенести встречу на вечер из-за пробки.

This is also correct, but it sounds a little less focused on the cause at the start.

Yes, very often.

• из-за пробки = because of a / the traffic jam
  often one specific jam on that occasion
• из-за пробок = because of traffic jams / heavy traffic
  more general or habitual

So the original sentence sounds like there was a specific traffic jam that caused the problem.

It can mean either, depending on context.

Literally, перенести is to move / transfer. With events like встреча, it often means:

• reschedule
• move
• sometimes postpone

In this sentence, because we know the new time is на вечер, reschedule or move is probably the best English match.

Sometimes, yes, but the meanings are slightly different.

• из-за пробки = because of a traffic jam
• из-за трафика = because of traffic

Трафик is used in modern Russian, but пробка / пробки is usually the more natural everyday word when talking about being stuck in traffic on the road.

So the original sentence sounds very natural.

The main word stresses are:

• из-за́
• про́бки
• нам
• пришло́сь
• перенести́
• встре́чу
• на
• ве́чер

So one possible stressed reading is:

Из-за́ про́бки нам пришло́сь перенести́ встре́чу на ве́чер.

This can help a lot with pronunciation and listening.