Η κουμπότρυπα είναι μεγάλη.

Η is the feminine singular definite article, meaning the.

So:

• η κουμπότρυπα = the buttonhole

It is capitalized here simply because it is the first word of the sentence. In the middle of a sentence, it would normally be written η.

Greek nouns have grammatical gender, and κουμπότρυπα is a feminine noun.

Greek definite articles change according to gender:

• ο = masculine the
• η = feminine the
• το = neuter the

Because κουμπότρυπα is feminine, it takes η in the nominative singular:

• η κουμπότρυπα

είναι is the verb to be.

In this sentence, it means is:

• Η κουμπότρυπα είναι μεγάλη.
• The buttonhole is big.

More specifically, είναι is the 3rd person singular form used for:

• he is
• she is
• it is

Greek uses the same form for all three.

μεγάλη is an adjective meaning big or large, and in Greek adjectives must agree with the noun they describe in:

• gender
• number
• case

Since κουμπότρυπα is:

• feminine
• singular
• nominative

the adjective must also be feminine singular nominative:

• μεγάλη

Compare:

• ο κήπος είναι μεγάλος = the garden is big
• η κουμπότρυπα είναι μεγάλη = the buttonhole is big
• το σπίτι είναι μεγάλο = the house is big

Because after the verb είναι (is), Greek commonly puts the adjective as a predicate adjective:

• Η κουμπότρυπα είναι μεγάλη.
• literally: The buttonhole is big.

This is normal and natural Greek word order.

Greek word order is often more flexible than English, but this version is the standard neutral one:

• subject + verb + adjective

A helpful approximate pronunciation is:

koom-BO-tree-pa

More roughly:

• κου = koo
• μπό = BO
• τρυ = tree
• πα = pa

A few useful notes:

• ου is pronounced like oo in food
• μπ inside a word is usually pronounced like b
• the accent mark shows the stressed syllable: μπό

So the stress is on BO:

• κου-ΜΠΟ-τρυ-πα

It is pronounced approximately:

EE-ne

or sometimes you may hear something close to EEN-eh, depending on speech style.

Important point: Even though it is spelled είναι, in modern Greek it is pronounced as two syllables, not three:

• εί-ναι in writing
• roughly EE-ne in pronunciation

The stress is on the first syllable:

• ΕΙναι

The accent mark shows which syllable is stressed.

So:

• κουμπότρυπα → stress on μπό
• είναι → stress on εί
• μεγάλη → stress on γά

This is very important in Greek, because stress is part of correct pronunciation and sometimes helps distinguish forms.

Yes, it is a compound word.

It comes from:

• κουμπί = button
• τρύπα = hole

So κουμπότρυπα literally means something like button-hole.

When words combine in Greek, their form often changes a little, so learners should not always expect the parts to stay exactly the same as in the dictionary forms.

Usually, if you mean the buttonhole, Greek uses the article:

• Η κουμπότρυπα είναι μεγάλη.

If you said:

• Κουμπότρυπα είναι μεγάλη,
  that would sound unnatural in ordinary neutral speech.

Greek uses the definite article more often than English does, so learners should get used to seeing ο / η / το frequently.

Yes. In many contexts, μεγάλη can be translated as either big or large.

So this sentence could be understood as:

• The buttonhole is big
• The buttonhole is large

Which English word sounds better depends on context and style, but the Greek adjective works for both.

No separate word for it is needed.

Greek often does not use subject pronouns unless they are needed for emphasis or contrast. The subject here is already expressed by the noun phrase:

• Η κουμπότρυπα = the buttonhole

So Greek does not need an extra word meaning it.

It is in the nominative singular.

That is because it is the subject of the sentence:

• Η κουμπότρυπα = the subject
• είναι = is
• μεγάλη = big

The article η also shows nominative singular feminine here.

Yes, Greek has some flexibility in word order, though the basic version is the most neutral:

• Η κουμπότρυπα είναι μεγάλη.

You might also see or hear:

• Μεγάλη είναι η κουμπότρυπα.

That can give a different emphasis, something like:

• It’s the buttonhole that is big
• or The buttonhole is big

But for a learner, the original order is the safest and most standard one to use.

You know it from the sentence structure and agreement.

In:

• Η κουμπότρυπα είναι μεγάλη

the noun phrase η κουμπότρυπα is the subject, and after είναι the adjective μεγάλη describes that subject.

Also, the adjective matches the noun in feminine singular form:

• κουμπότρυπα → feminine singular
• μεγάλη → feminine singular

That agreement helps Greek speakers connect the adjective to the noun.