Luna hodie clarior est quam heri.

Because luna is the subject of the sentence: it is the thing being described as brighter.

• luna = nominative singular feminine
• It goes with est = is
• So the basic structure is: The moon is brighter

Latin marks the subject with the nominative case, just as English usually marks it by word order.

Because clarior is the comparative form of clarus, clara, clarum.

• clara = bright
• clarior = brighter

The sentence is making a comparison: the moon is brighter today than yesterday, so Latin uses the comparative adjective.

Because clarior is the nominative singular form used for masculine and feminine, while clarius is neuter.

Since luna is feminine, the adjective must agree with it:

• feminine subject: luna
• feminine comparative form: clarior

So clarior is the correct form here.

Yes. Comparatives in Latin are a little unusual:

• the positive adjective clarus, clara, clarum is a 1st/2nd-declension adjective
• but its comparative clarior, clarius declines like a third-declension adjective

Even so, it still agrees with luna in gender, number, and case.

Here both are effectively:

• feminine
• singular
• nominative

So the agreement is correct, even though the ending looks different from clara.

Quam means than.

It is the standard word used to introduce the second part of a comparison after a comparative adjective:

• clarior quam heri = brighter than yesterday

So once you see a comparative like clarior, seeing quam afterward is very common and expected.

Because Latin is compressing a fuller idea.

The full sense is:

• Luna hodie clarior est quam heri erat.
• The moon is brighter today than it was yesterday.

But Latin often leaves out words that are easy to understand from context. So heri here is shorthand for yesterday / than it was yesterday.

This is very natural in both Latin and English:

• brighter than yesterday really means
• brighter than it was yesterday

They are both adverbs of time.

• hodie = today
• heri = yesterday

They do not change form for case, number, or gender. They are indeclinable.

In this sentence:

• hodie tells you when the moon is brighter
• heri gives the earlier time used for comparison

Est is the 3rd person singular of sum, meaning is.

It links the subject and the predicate adjective:

• Luna ... clarior est
• The moon is brighter

Latin sometimes does omit forms of sum, especially in poetry or in very compressed style, but in an ordinary straightforward sentence, including est is completely normal.

So here est makes the sentence explicit and clear.

Yes, Latin word order is much more flexible than English word order.

This sentence is arranged in a very natural way, but other orders are possible, for example:

• Hodie luna clarior est quam heri
• Luna clarior hodie est quam heri

The meaning stays basically the same because Latin uses endings and forms, not just position, to show relationships.

Still, this order sounds very natural:

• luna first introduces the topic
• hodie highlights today
• clarior comes before est, which is very common
• quam heri finishes the comparison

Because Latin has no articles.

There is no separate word for:

• the
• a
• an

So luna can mean:

• moon
• the moon
• sometimes even a moon

The context tells you which is best in English. In this sentence, English naturally says the moon.

Not naturally in this sentence, because heri is an adverb, not a noun in the ablative.

Latin often has two ways to make a comparison:

• comparative + quam
• comparative + ablative of comparison

For example, with a noun you might compare something to something else without quam. But here the comparison is with yesterday, a time adverb, so quam heri is the natural construction.

Really the sentence means:

• brighter than it was yesterday and quam is the right tool for that.

No. Clarus has a wider range of meanings, including:

• bright
• clear
• famous
• renowned

But with luna, the meaning bright is the most natural one.

So clarior here means brighter, not more famous or clearer. Context decides which sense is intended.