Μετά τη βροχή βγήκε ένα ουράνιο τόξο, και όλοι στην πλατεία το κοιτούσαν.

Because μετά here is a preposition meaning after, and it takes the accusative case in Modern Greek.

So:

• η βροχή = the rain as the subject form (nominative)
• τη βροχή = the rain after a preposition like μετά (accusative)

You will often see:

• μετά το μάθημα = after the lesson
• μετά τη βροχή = after the rain

Also, τη is the usual form here rather than την, because the following word begins with β.

Both are possible in Modern Greek.

• μετά τη βροχή
• μετά από τη βροχή

Both mean after the rain.
In everyday Greek, μετά από is very common, but μετά by itself is also completely normal and often a bit more compact.

So this sentence is not unusual at all. It is just using the shorter version.

Βγήκε is the aorist of βγαίνω, which literally means to go out / come out.

But in Greek, it is also very natural to use βγαίνω for things that appear in the sky or become visible, such as:

• βγήκε ο ήλιος = the sun came out
• βγήκε το φεγγάρι = the moon came out
• βγήκε ένα ουράνιο τόξο = a rainbow appeared / came out

So here βγήκε does not mean that the rainbow physically went somewhere. It means it appeared.

Greek word order is more flexible than English word order.

Putting the verb first, as in βγήκε ένα ουράνιο τόξο, sounds very natural when you are introducing something new into the scene. It is a bit like saying:

• There appeared a rainbow
• A rainbow came out

So the order helps present ένα ουράνιο τόξο as new information.

Both orders are possible, but βγήκε ένα ουράνιο τόξο is especially natural in narration.

It is two words:

• ουράνιο = heavenly / celestial
• τόξο = bow

Together, ουράνιο τόξο means rainbow.

It behaves like a normal noun phrase, and both words are neuter singular here:

• ένα = a/an (neuter singular)
• ουράνιο = neuter singular adjective
• τόξο = neuter singular noun

So everything agrees grammatically.

Όλοι by itself can mean everyone or all of them, depending on context.

Here, it means something like everyone or all the people there. Greek often leaves nouns understood when they are obvious from the situation.

So:

• όλοι στην πλατεία = everyone in the square

There is no need to add οι άνθρωποι unless you want to be more explicit.

Also, Greek usually does not need a separate subject pronoun like they, because the verb ending already shows the person and number.

Because Greek often uses the plural form όλοι to express the idea of everyone / all the people.

Literally, it is closer to all or all of them, but in many contexts English naturally translates it as everyone.

Also note:

• όλοι = masculine plural
• όλες = feminine plural
• όλα = neuter plural

The masculine plural is the normal default for a mixed group or for people in general.

Στην is a contraction of:

• σε = in / at / to
• την = the (feminine accusative)

So:

• σε την πλατεία → στην πλατεία

This contraction is standard and extremely common.

A few similar examples:

• στο σπίτι = in/to the house
• στην πόλη = in/to the city
• στους δρόμους = in/to the streets

Yes. After σε, Greek normally uses the accusative.

So:

• η πλατεία = the square (nominative)
• την πλατεία = the square (accusative)

And with the preposition:

• στην πλατεία = in the square / at the square

This is very common in Greek: σε can cover meanings that English expresses with in, at, on, or to, depending on context.

Το is the object pronoun meaning it.

It refers back to ένα ουράνιο τόξο, which is neuter singular, so the pronoun is also neuter singular:

• το ουράνιο τόξο → το

So:

• το κοιτούσαν = they were looking at it

This is very typical Greek. Once the noun has been mentioned, Greek often uses a short clitic pronoun like το, τον, την, etc.

Because κοιτούσαν is the imperfect, which describes an ongoing, repeated, or background action in the past.

So the sentence presents two different past actions:

• βγήκε = aorist → the rainbow appeared as a single event
• κοιτούσαν = imperfect → people were watching it for some time

This combination is very common in storytelling:

• aorist for the event that happens
• imperfect for the ongoing background action

If you said το κοίταξαν, that would sound more like they looked at it as a single completed action, not as an ongoing scene.

Not exactly.

• κοιτάω / κοιτώ = look at
• βλέπω = see

So:

• το κοιτούσαν = they were looking at it
• το έβλεπαν = they were seeing it

In this sentence, κοιτούσαν is better because it shows an active action: people had their eyes on the rainbow and were watching it.

Because Greek is a pro-drop language, which means subject pronouns are often omitted.

The verb ending already tells you the subject is they:

• κοιτούσαν = they were looking

And in this sentence, the subject is already stated explicitly as όλοι στην πλατεία, so adding αυτοί would usually be unnecessary.

Greek only adds subject pronouns when there is special emphasis or contrast.