Αυτό το πεδίο είναι σημαντικό.

Because πεδίο is a neuter singular noun.

In Greek, words like this must agree with the noun they describe in gender, number, and case.

For this in the nominative singular:

• αυτός = masculine
• αυτή = feminine
• αυτό = neuter

Since το πεδίο is neuter singular, Greek uses αυτό.

Greek commonly uses both the demonstrative and the definite article together:

• αυτό το πεδίο = this field

So:

• αυτό = this
• το = the
• πεδίο = field

This is normal Greek structure. English says just this field, but Greek usually says literally something like this the field.

Πεδίο is neuter.

A common clue is the article:

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

Here we have το πεδίο, so the noun is neuter.

Also, many neuter nouns in Greek end in -ο, though this is not the only neuter ending.

Because adjectives in Greek must agree with the noun they describe.

Since πεδίο is:

• neuter
• singular
• nominative

the adjective must also be neuter singular nominative:

• σημαντικός = masculine
• σημαντική = feminine
• σημαντικό = neuter

So σημαντικό matches πεδίο.

Greek does not have an indefinite article like English a/an.

It has a definite article:

• ο, η, το = the

But for a/an, Greek usually just uses the noun without a special article.

So Greek distinguishes:

• το πεδίο = the field
• πεδίο = a field or just field, depending on context

In your sentence, it is this field, so the definite article appears as part of αυτό το πεδίο.

Είναι means is.

It is the 3rd person singular form of είμαι = I am / to be.

So:

• Αυτό το πεδίο = this field
• είναι = is
• σημαντικό = important

Unlike in some languages, Greek usually keeps the verb to be in sentences like this.

In normal standard Greek, this sentence is most naturally:

• Αυτό το πεδίο είναι σημαντικό.

Leaving out είναι would usually sound incomplete in ordinary prose or speech.

Greek can omit subjects quite often, but not usually the verb to be in a sentence like this.

Not completely. Greek word order is more flexible than English.

The neutral, straightforward order is:

• Αυτό το πεδίο είναι σημαντικό.

But other orders are possible for emphasis, for example:

• Σημαντικό είναι αυτό το πεδίο.
• Αυτό το πεδίο σημαντικό είναι. (less neutral, more marked)

A learner should usually stick with:

• subject + είναι + adjective

That is the safest and most natural pattern.

A simple learner-friendly pronunciation guide:

• Αυτό ≈ af-TO
• το ≈ to
• πεδίο ≈ pe-THEE-o
• είναι ≈ EE-ne
• σημαντικό ≈ see-man-dee-KO

A few helpful notes:

• δ in Modern Greek sounds like th in this
• θ sounds like th in think
• The accented syllable is stressed:
  • αυτό
  • πεδίο
  • είναι
  • σημαντικό

Because it is pronounced πε-δί-ο.

The letters ι and ο here do not combine into one syllable; they are pronounced separately.

So:

• πεδίο = pe-DI-o

This is common in some Greek words where vowel letters stand next to each other but are still pronounced in separate syllables.

It is in the nominative singular.

You can tell because it is the subject of the sentence:

• This field is important.

In Greek, the subject is normally in the nominative case.

So in this sentence:

• αυτό το πεδίο = nominative singular neuter

And the adjective σημαντικό agrees with it.

Yes.

That would mean:

• The field is important.

The difference is:

• Αυτό το πεδίο είναι σημαντικό. = This field is important.
• Το πεδίο είναι σημαντικό. = The field is important.

So αυτό adds the idea of this.

No. Πεδίο can mean several things depending on context, including:

• a physical field
• an area
• a domain
• a field of study
• a field in a form or database
• a scientific field, like a magnetic field

So although the sentence structure is simple, the noun itself can be used in many contexts.

Greek uses accent marks to show which syllable is stressed.

• αυτό has stress on the last syllable, so it needs an accent
• το is a short unstressed article, so it has no accent

The accent is important in Greek spelling and often helps you pronounce the word correctly.

Here it is an adjective.

It describes the noun πεδίο:

• important field
• the field is important

Greek adjectives change form to match the noun, which is exactly what happens here with σημαντικό.

An adverb would describe a verb, not a noun.

Yes, in other contexts αυτό can also function as a pronoun, meaning this or it/that thing depending on usage.

But in this sentence, it is clearly a demonstrative determiner modifying πεδίο:

• αυτό το πεδίο = this field

So here it is not standing alone; it is directly attached to the noun phrase.