Η γιαγιά μου αλλάζει το νερό στο βάζο κάθε δύο μέρες, για να μένουν φρέσκα τα λουλούδια.

Μου means my here.

In Modern Greek, possession is often shown with a short unstressed pronoun placed after the noun:

• η γιαγιά μου = my grandmother
• το σπίτι μου = my house

So Greek says something more like the grandmother my, but in natural English we translate it as my grandmother.

Greek normally keeps the definite article with nouns even when a possessive like μου is present.

So:

• η γιαγιά μου = my grandmother
• ο φίλος μου = my friend
• το βιβλίο μου = my book

This is just standard Greek structure. It sounds completely normal in Greek, even though English does it differently.

In this context, it means replaces/changes the water.

Greek uses αλλάζω very naturally for replacing something with fresh/new something:

• αλλάζω το νερό = change/replace the water
• αλλάζω ρούχα = change clothes
• αλλάζω λάμπα = change a light bulb

So here the idea is that she empties the old water and puts in fresh water.

Because Greek present tense can describe a habitual or repeated action, not just something happening right now.

Here the phrase κάθε δύο μέρες shows that this is a routine:

• Η γιαγιά μου αλλάζει... κάθε δύο μέρες
  = My grandmother changes... every two days

So the present tense works just like English present simple for habits.

Το νερό is the direct object of αλλάζει, so it is in the accusative case.

However, because νερό is a neuter noun, its nominative and accusative forms are the same:

• nominative: το νερό
• accusative: το νερό

So even though the form does not change, its role in the sentence is object: she changes the water.

Στο is a contraction of:

• σε + το = στο

The preposition σε can mean in, at, to, or on, depending on context.

So:

• στο βάζο = in the vase

This contraction is very common in Greek:

• στο σπίτι = in/at the house
• στο σχολείο = at/to school

Here it means in the vase.

The preposition σε is broader than any single English preposition, so you choose the best English translation from context. In this sentence, there is no movement to the vase being emphasized; the phrase identifies where the water is:

• το νερό στο βάζο = the water in the vase

So the whole idea is: she changes the water that is in the vase.

Κάθε means every/each, and the whole phrase κάθε δύο μέρες is the normal way to say every two days.

Literally:

• κάθε = every
• δύο = two
• μέρες = days

So the pattern is:

• κάθε μέρα = every day
• κάθε δύο μέρες = every two days
• κάθε εβδομάδα = every week

Also, μέρες is the everyday form of ημέρες. Both are understood, but μέρες sounds very natural in speech.

Για να means so that or in order to. It introduces a purpose clause.

So:

• για να μένουν φρέσκα τα λουλούδια
  = so that the flowers stay fresh

It answers the question why she changes the water.

Because Modern Greek normally does not use an infinitive the way English does.

Instead, Greek uses:

• να + finite verb

So where English says:

• to stay fresh

Greek says:

• να μένουν φρέσκα

After για να, the verb is in the subjunctive environment. In many verbs, that form looks exactly like the ordinary present form, which is what you see here.

Because the subject is plural: τα λουλούδια = the flowers.

Greek verbs agree with their subject in number:

• μένει = he/she/it stays
• μένουν = they stay

So:

• τα λουλούδια μένουν = the flowers stay

Even though τα λουλούδια comes later in the sentence, it is still the subject of μένουν.

Because μένουν means stay/remain, which fits the idea much better.

The point is not just that the flowers are fresh at one moment, but that changing the water helps them remain fresh over time.

So:

• είναι φρέσκα = are fresh
• μένουν φρέσκα = stay/remain fresh

In this sentence, μένουν is the more natural and precise choice.

Because it agrees with τα λουλούδια, which is neuter plural.

Greek adjectives agree with the noun they describe in gender, number, and case.

Here:

• τα λουλούδια = neuter plural
• φρέσκα = neuter plural form of fresh

So:

• φρέσκο λουλούδι = fresh flower
• φρέσκα λουλούδια = fresh flowers

Even though φρέσκα comes after the verb, it still agrees with the subject.

Greek word order is more flexible than English word order.

The phrase:

• για να μένουν φρέσκα τα λουλούδια

is perfectly natural. The subject τα λουλούδια comes after the verb, which is very common in Greek.

This order keeps the flow smooth and puts a little emphasis on the result first:

• μένουν φρέσκα = stay fresh

Then the sentence finishes by naming what stays fresh:

• τα λουλούδια = the flowers

So the order is natural Greek, not unusual or poetic.