Quies puero aegro maxime prodest.

The subject is quies.

You can tell because:

• it is in the nominative singular
• the verb prodest is singular, so it needs a singular subject
• the meaning also fits: rest is the thing that does good / is beneficial

So the core structure is:

• quies = the subject
• prodest = the verb
• puero aegro = the person to whom it is beneficial

That is a very common question. In Latin, -es does often mark a plural, but not always.

Here, quies is a third-declension noun whose nominative singular just happens to be quies. Its dictionary form is:

• quies, quietis = rest, quiet

So in this sentence, quies is singular, not plural.

This is a good reminder that you cannot identify case and number from the ending alone in every situation; sometimes you also need:

• the dictionary form
• the verb agreement
• the overall sense of the sentence

Because aegro is an adjective describing puero, and adjectives agree with the nouns they modify in:

• case
• number
• gender

So:

• puero = to/for the boy or for the sick boy depending on context
• aegro = sick, agreeing with puero

Both are:

• dative singular
• masculine

Together they mean to/for the sick boy.

Because the verb prodest takes the dative of the person who receives the benefit.

The verb comes from prosum, prodesse, which means:

• to be useful
• to do good
• to benefit

In Latin, the person benefited is normally put in the dative:

• alicui prodest = it benefits someone
• literally, it is useful to someone

So puero aegro means to the sick boy or for the sick boy, not a direct object.

Prodest is the third-person singular present active indicative of prosum, prodesse, profui.

It means something like:

• is beneficial
• does good
• helps

It is an irregular compound of sum with the prefix pro-.

So:

• sum = I am
• prosum = I am useful / I benefit
• prodest = he/she/it is useful / benefits

A useful thing to notice is that the form is built from pro- + est, giving prodest.

Maxime is an adverb, and it modifies prodest.

Here it means something like:

• most
• especially
• very greatly

So it strengthens the idea of benefit: rest is especially beneficial.

It is not describing a noun. If it were an adjective, it would have to agree with a noun in case, number, and gender. But maxime stays the same because it is an adverb.

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

This sentence puts:

• quies first, which gives it some emphasis
• prodest at the end, which is very common in Latin
• maxime right before the verb, which neatly emphasizes the verb

Other word orders would also be possible, for example:

• Puero aegro quies maxime prodest
• Quies maxime puero aegro prodest

These would all mean basically the same thing, though the emphasis would shift a little.

So the order here is natural Latin, but not the only possible order.

In some contexts, yes, an adjective can stand by itself and mean something like the sick man or the sick person.

But here, because puero is present, the normal reading is that aegro modifies puero:

• puero aegro = to the sick boy

So in this sentence they go together as one phrase.

A helpful parsing is:

• quies — nominative singular feminine noun, the subject
• puero — dative singular masculine noun
• aegro — dative singular masculine adjective modifying puero
• maxime — adverb, modifying prodest
• prodest — 3rd person singular present active indicative of prosum

So the pattern is:

• subject
  • dative of the person benefited
    • adverb
      • verb

That pattern is worth remembering, because prosum / prodesse regularly works this way in Latin.