Błyskawica była tak jasna, że dzieci obudziły się w nocy.

Because błyskawica is a feminine singular noun in Polish, and the past tense of być (to be) must agree with it.

• był = masculine singular
• była = feminine singular
• było = neuter singular

So:

• Błyskawica była jasna = The lightning was bright

The adjective must agree with the noun it describes.

Since błyskawica is:

• feminine
• singular
• nominative

the adjective also has to be feminine singular nominative:

• jasny = masculine
• jasna = feminine
• jasne = neuter

So błyskawica była jasna is the correct agreement.

This is a very common Polish structure meaning so ... that ...

In this sentence:

• tak jasna = so bright
• że = that

So:

• Błyskawica była tak jasna, że... = The lightning was so bright that...

You can use this pattern with many adjectives:

• Był tak zmęczony, że zasnął. = He was so tired that he fell asleep.
• Film był tak nudny, że wyszliśmy. = The film was so boring that we left.

Obudziły się means woke up.

The base verb is obudzić = to wake someone up.
With się, it becomes reflexive:

• obudzić kogoś = to wake someone
• obudzić się = to wake up

So:

• Mama obudziła dzieci. = Mom woke the children up.
• Dzieci obudziły się. = The children woke up.

Because in Polish, to wake up is usually expressed with the reflexive verb obudzić się.

English often uses a different verb pair:

• wake someone up
• wake up

Polish often uses:

• obudzić kogoś
• obudzić się

So się shows that the action happened to the subject itself: the children woke themselves, meaning simply they woke up.

Because dzieci takes non-masculine-personal plural agreement in standard Polish grammar.

In the past tense plural, Polish distinguishes:

• -li for masculine-personal groups
• -ły for non-masculine-personal groups

Even though dzieci refers to people, it normally goes with:

• dzieci były
• dzieci obudziły się

not:

• dzieci byli
• dzieci obudzili się

This is just how the noun dzieci behaves grammatically.

W nocy is the normal expression meaning at night or during the night.

Here, w is followed by the locative case, so noc becomes nocy.

• noc = night
• w nocy = at night / during the night

This is a fixed and very common phrase.

Compare:

• w dzień = during the day / in the daytime
• w nocy = at night

Usually the most natural English translation is at night or during the night.

In this sentence, it means that the children woke up during the night, not necessarily that night is being contrasted with day in a very general sense.

So a natural translation is:

• The lightning was so bright that the children woke up during the night.
• or more simply: ...woke up at night.

Yes. Błyskawica commonly means lightning or a flash of lightning.

A related word is piorun, which often means:

• thunderbolt
• lightning strike

Very roughly:

• błyskawica focuses more on the flash
• piorun can sound more like the strike itself

But in many everyday contexts, błyskawica is a perfectly normal word for lightning.

Yes, Polish word order is more flexible than English word order.

The given sentence is natural:

• Błyskawica była tak jasna, że dzieci obudziły się w nocy.

But other versions are also possible, depending on emphasis:

• W nocy dzieci obudziły się, bo błyskawica była tak jasna.
• Dzieci obudziły się w nocy, bo błyskawica była tak jasna.

Polish uses endings more than word order to show grammatical relationships, so changing the order often changes focus rather than basic meaning.

Obudziły się is perfective.

That means it presents the action as a completed event:

• obudziły się = they woke up

If you used an imperfective form such as budziły się, it would suggest a repeated, ongoing, or less bounded action, depending on context.

So here the perfective is appropriate because the sentence describes a specific completed event: the lightning flashed, and the children woke up.

A rough English-friendly guide:

• Błyskawica ≈ bwih-ska-VEE-tsa
• była ≈ BIH-wa
• tak = tahk
• jasna ≈ YAS-na
• że ≈ zheh
• dzieci ≈ DZHYE-chee
• obudziły się ≈ oh-boo-JIH-wih shyeh
• w nocy ≈ v NO-tsih

A few useful pronunciation notes:

• ł sounds like English w
• j sounds like English y
• cz / ci / ć / dzi / dź-type sounds are often softer than English speakers expect
• ę and ą are nasal vowels, though in connected speech they often change depending on the following sound

Yes, that is exactly the idea.

The structure:

• Błyskawica była tak jasna, że dzieci obudziły się w nocy

means the lightning was so bright that as a result the children woke up.

So the sentence expresses a cause-and-result relationship:

• cause: the lightning was very bright
• result: the children woke up