К счастью, мы успели на поезд, потому что вышли пораньше.

К счастью means fortunately or luckily.

It is an introductory phrase, so it is set off with a comma: К счастью, ...

Literally, it is related to счастье (happiness, good fortune), but you should treat к счастью as a fixed expression meaning fortunately, not translate it word for word.

Успели is the past plural form of успеть.

In this sentence, успеть means to make it in time, to manage to catch, or to be in time for something.

So:

• мы успели на поезд = we made it in time for the train / we managed to catch the train

This is very natural Russian. Russian often uses успеть на поезд / на автобус / на самолёт, where English might say catch the train/bus/plane.

Успели is perfective.

That fits because the sentence talks about a completed result:

• we did make it to the train

The imperfective partner is успевать. That would usually be used for repeated situations, process, or general ability:

• Я часто успеваю на поезд. = I often make it to the train on time.

Here, though, we are talking about one finished event, so успели is the right choice.

It is accusative case after на:

• на поезд

With успеть на + transport/event, Russian means to be in time for that thing:

• успеть на поезд = make it in time for the train
• успеть на автобус = make it in time for the bus
• успеть на урок = make it in time for class

A useful detail: поезд is an inanimate masculine noun, so its accusative singular looks the same as the nominative singular. That is why you see поезд, not a visibly different form.

Because успеть на поезд is the normal idiomatic way to express this idea.

If you translate English too literally, you may look for a verb meaning catch, but Russian usually expresses the idea as being in time for the train.

A verb like поймать usually means catch physically, like:

• поймать мяч = catch a ball
• поймать рыбу = catch a fish

So поймать поезд would not be the normal choice here.

Because the subject is мы (we).

In the past tense, Russian verbs agree in number and, in the singular, also in gender:

• я успел / я успела
• мы успели

And similarly:

• он вышел
• она вышла
• они / мы вышли

So успели and вышли are plural because the subject is мы.

Вышли is the perfective past form of выйти.

It is used because this was a single completed action:

• they left earlier, and that led to the result of catching the train

If you used выходили instead, it would sound more like:

• a repeated action
• a habitual action
• or focus on the process rather than the completed event

So in this sentence, вышли is the natural choice.

Пораньше means a bit earlier, somewhat earlier, or earlier than usual/planned.

Compare:

• раньше = earlier
• пораньше = a little earlier / nice and early

Пораньше often sounds a bit softer and more conversational. In this sentence, it suggests:

• we left a little earlier than we otherwise would have

So:

• вышли пораньше = left a bit earlier

Both verbs can relate to leaving, but the nuance is different.

• выйти = to go out, to step out, to exit
• уйти = to leave, to go away

In this sentence, вышли suggests leaving the place you were in, such as home or a building, in order to go catch the train. That is very natural in Russian.

If you said ушли, the focus would be more on the fact of departing rather than stepping out from a place. It is not impossible in some contexts, but вышли пораньше is very natural here.

Because потому что introduces a subordinate clause:

• ..., потому что вышли пораньше.
• ..., because we left earlier.

Russian normally puts a comma before потому что, just as English separates a because clause in many similar sentence structures.

So the sentence has:

1. a comma after the introductory phrase К счастью
2. a comma before the subordinate clause introduced by потому что

Yes. Russian word order is fairly flexible because the grammatical endings carry a lot of the meaning.

For example, you could also say:

• Мы, к счастью, успели на поезд, потому что вышли пораньше.
• Потому что мы вышли пораньше, мы успели на поезд.

The original version is very natural and neutral:

• К счастью, мы успели на поезд, потому что вышли пораньше.

Changing the order usually changes the focus or emphasis, not the basic meaning.

Usually it strongly suggests that they did make it in time and caught it.

However, the core meaning is they were not too late for the train.

If you want to be extra explicit about boarding, Russian can say:

• Мы успели сесть на поезд. = We managed to get on the train in time.

So:

• успели на поезд = we made it in time for the train
• успели сесть на поезд = we managed to board the train in time

A helpful stress pattern is:

К сча́стью, мы успе́ли на по́езд, потому́ что вы́шли пора́ньше.

A few pronunciation notes:

• сча́стью has a consonant cluster that can be tricky for English speakers
• успе́ли is stressed on -пе́-
• по́езд is stressed on the first syllable
• вы́шли is stressed on the first syllable
• пора́ньше is stressed on -ра́нь-

If you say it slowly with the stress in the right place, it will sound much more natural.