Demokratio gravas por la socio.

Because demokratio is being used as a general concept: democracy in the abstract, not the democracy of one specific country or situation.

In Esperanto, you often leave out la when talking about something in a broad, general sense.

• Demokratio gravas = Democracy is important
• La demokratio de tiu lando = The democracy of that country

So here, Demokratio means democracy in general.

Gravas comes from the root grav-, which has the idea of importance or seriousness.

The ending -as is the present-tense verb ending in Esperanto. So:

• gravas = is important / matters
• gravis = was important
• gravos = will be important

A useful thing to notice is that Esperanto can turn an idea like important into a verb:

• Ĝi estas grava = It is important
• Ĝi gravas = It matters / It is important

Both are possible, but gravas is very natural.

Both are correct, but they are slightly different in structure:

• Demokratio estas grava por la socio.
• Demokratio gravas por la socio.

The first uses grava as an adjective: Democracy is important.
The second uses gravas as a verb: Democracy matters / is important.

Esperanto often allows both styles. In this sentence, gravas is a compact and natural way to express the idea.

The subject is Demokratio.

That is the thing doing the verb gravas. In other words, democracy is the thing that matters / is important.

So the structure is:

• Demokratio = subject
• gravas = verb
• por la socio = prepositional phrase explaining for society

Because there is no direct object here.

The -n ending in Esperanto usually marks the direct object. But in this sentence:

• Demokratio is the subject
• gravas is an intransitive-style verb here
• por la socio is a prepositional phrase

Since por already introduces the phrase la socio, you do not add -n to socio.

So:

• la socio is correct
• la socion would be wrong here

Por usually means for in the sense of for the benefit of, for the sake of, or with regard to usefulness or importance.

So gravas por la socio means is important for society.

By contrast:

• al usually means to or toward
• por means for

So por is the natural choice here because the sentence is talking about what is beneficial or important for society.

La socio means society.

Even though English often says just society without an article, Esperanto often uses la with nouns like this when referring to the institution or whole concept as a recognizable thing.

So:

• por socio would sound less natural here
• por la socio is the normal wording

In many abstract or collective cases, Esperanto uses la where English may not.

Yes. Esperanto word order is fairly flexible, because endings and prepositions make the roles clear.

For example, these are possible:

• Demokratio gravas por la socio.
• Por la socio gravas demokratio.

But the original order is the most straightforward and neutral for a learner: subject + verb + rest of sentence.

A rough pronunciation guide is:

de-mo-kra-TEE-o GRAH-vas por lah so-TSI-o

A few helpful points:

• ti before o in demokratio is pronounced clearly as tee-o
• gr in gravas is pronounced with both consonants
• c in socio sounds like ts
• stress in Esperanto is always on the second-to-last syllable

So:

• de-mo-kra-TI-o
• GRA-vas
• SO-ci-o

Yes. It is a very transparent cognate.

• English: society
• Esperanto: socio

That makes it easier to recognize, but remember the pronunciation is Esperanto-style, especially the c, which sounds like ts.

Yes. That is a very good way to feel the sentence naturally.

Demokratio gravas can be understood as:

• Democracy is important
• Democracy matters

That is one reason the verb gravi is so useful in Esperanto: it often sounds very natural where English might choose either an adjective phrase or the verb matter.

Yes, very much so. It is short, natural, and idiomatic.

Esperanto often prefers concise structures like:

• Tio gravas. = That matters.
• Edukado gravas. = Education is important.
• Libereco gravas por homoj. = Freedom is important for people.

So Demokratio gravas por la socio is a very normal Esperanto sentence pattern.