Μετά τη βόλτα στο πάρκο, η δίψα μου ήταν τόσο μεγάλη που ήπια δύο ποτήρια νερό.

Here μετά means after, and in that meaning it takes the accusative.

So:

• η βόλτα = the walk / the outing (nominative)
• τη βόλτα = the walk (accusative)

That is why you get:

• Μετά τη βόλτα = After the walk

A useful contrast:

• μετά + accusative = after
• μετά από + accusative = also after, very common in modern Greek

So you may also hear:

• Μετά από τη βόλτα...

Both are natural.

Βόλτα is a very common Greek word, but it is a bit broader than English walk.

It can mean:

• walk
• stroll
• outing
• little trip around
• going out for a bit

So τη βόλτα στο πάρκο most naturally means something like:

• the walk in the park
• the outing in the park
• the stroll in the park

You will often see βόλτα in expressions like:

• πάω βόλτα = I go for a walk / I go out
• κάνω βόλτα = I take a walk / I go घूम...
  More naturally in English: I go for a walk / I take a stroll

Στο is a contraction of:

• σε + το = στο

So:

• σε = in / at / to
• το πάρκο = the park
• στο πάρκο = in the park / at the park / to the park

In this sentence, στο πάρκο is best understood as in the park.

This contraction is extremely common:

• στο = σε το
• στη = σε τη(ν)
• στον = σε τον
• στους = σε τους, etc.

Η δίψα μου literally means the thirst of mine, i.e. my thirst.

In Greek, possessive words like μου often come after the noun:

• η δίψα μου = my thirst
• το σπίτι μου = my house
• η φίλη μου = my friend

That is the normal everyday pattern.

Greek can sometimes change word order for emphasis, but η δίψα μου is the standard, neutral way to say my thirst.

Greek often expresses ideas with a noun where English might prefer an adjective.

So instead of:

• I was very thirsty

Greek can naturally say:

• My thirst was so great...

That is exactly what happens here:

• η δίψα μου ήταν τόσο μεγάλη = my thirst was so great

This is a very Greek-sounding way to express the idea.

A more direct alternative also exists, for example:

• Διψούσα τόσο πολύ που... = I was so thirsty that...

Both are natural, but the sentence you were given uses the noun δίψα.

Μεγάλη agrees with δίψα.

• δίψα is feminine singular
• so the adjective must also be feminine singular

That is why we get:

• η μεγάλη δίψα
• η δίψα ήταν μεγάλη

Here it means great / strong / intense, not literally physically big.

So:

• τόσο μεγάλη δίψα = such great thirst / such intense thirst

This is a very normal Greek collocation.

This is a very common Greek structure meaning:

• so ... that ...

In your sentence:

• τόσο μεγάλη που ήπια...
• so great that I drank...

So the full structure is:

• η δίψα μου ήταν τόσο μεγάλη που...
• my thirst was so great that...

You can use τόσο ... που ... with adjectives, adverbs, and more:

• Ήταν τόσο κουρασμένος που κοιμήθηκε αμέσως.
  He was so tired that he fell asleep immediately.

• Έτρεχε τόσο γρήγορα που δεν τον έφτασα.
  He was running so fast that I couldn’t catch him.

Very useful pattern.

Yes. Ήπια is the aorist form of the verb πίνω (to drink).

This verb is irregular, so the forms change quite a bit:

• πίνω = I drink / I am drinking
• ήπια = I drank

So in the sentence:

• ήπια δύο ποτήρια νερό
• I drank two glasses of water

This is a good verb to memorize as a pair:

• πίνω — ήπια

Because ήπια is aorist, and here the action is seen as a single completed event:

• I drank two glasses of water

That is exactly the kind of thing Greek usually expresses with the aorist.

Compare:

• ήπια = I drank / completed action
• έπινα = I was drinking / I used to drink / ongoing, repeated, or background action

In this sentence, the point is the result of the thirst: one completed action followed from it. So ήπια is the natural choice.

In modern everyday Greek, after a container or measure noun, the substance often appears in its basic form rather than in the genitive.

So Greek commonly says:

• ένα ποτήρι νερό = a glass of water
• δύο ποτήρια νερό = two glasses of water
• ένα μπουκάλι κρασί = a bottle of wine

So ποτήρια νερό is a normal modern pattern.

About the forms:

• δύο = two
• ποτήρια = glasses (accusative plural of ποτήρι)
• νερό = water

This whole phrase functions as the object of ήπια.

Ήταν is the imperfect of είμαι (to be), third person singular:

• ήταν = was

It is used because it describes a state in the past:

• η δίψα μου ήταν τόσο μεγάλη...
• my thirst was so great...

So the sentence combines:

• a background state: ήταν
• a completed action: ήπια

That combination is very common in Greek narrative:

• state/background in the imperfect
• main event in the aorist

Yes, it is natural and helpful.

The phrase:

• Μετά τη βόλτα στο πάρκο

is an introductory time phrase: After the walk in the park.

Greek often uses a comma after such introductory phrases, especially when they are a bit longer. It works much like English punctuation here.

So the comma helps separate:

• the setting/time phrase from
• the main clause

It is not a grammar mystery; it is mostly punctuation for clarity and rhythm.

Yes. Greek often allows several natural alternatives. For example:

• Μετά τη βόλτα στο πάρκο, διψούσα τόσο πολύ που ήπια δύο ποτήρια νερό.
  After the walk in the park, I was so thirsty that I drank two glasses of water.

• Μετά τη βόλτα στο πάρκο, ήμουν τόσο διψασμένος / διψασμένη που ήπια δύο ποτήρια νερό.
  After the walk in the park, I was so thirsty that I drank two glasses of water.

But your original sentence is perfectly natural and has a slightly more expressive feel because it focuses on the thirst itself:

• η δίψα μου ήταν τόσο μεγάλη...