Puer peius dormit, quia tonitrum audit.

Puer is nominative singular, and it is the subject of the sentence: the boy is the one doing the sleeping and hearing.

A few useful details:

• puer = boy
• It is a 2nd-declension masculine noun
• Its nominative singular is simply puer

So in Puer peius dormit, puer means the boy or a boy, depending on context.

Latin has no articles—there is no exact equivalent of the or a/an.

So puer can mean:

• the boy
• a boy

Which one is best depends on context. In a simple sentence like this, English often uses the boy, but Latin does not need a separate word for that.

Because peius here is an adverb, not an adjective.

It modifies dormit (sleeps), so it tells us how he sleeps:

• male = badly
• peius = worse / more badly
• pessime = worst / very badly

By contrast, peior is usually the adjective form meaning worse:

• puer peior = a worse boy
• peius dormit = he sleeps worse

So the sentence needs the adverb peius, because it is describing the verb dormit.

It means the comparative idea sleeps worse.

In English, worse can function naturally here, even though logically it is the comparative of badly. Latin uses peius as the comparative adverb, so the sense is:

• he sleeps worse
• he sleeps more badly

Both reflect the grammar, but he sleeps worse is better English.

Dormit is:

• 3rd person singular
• present tense
• active voice
• indicative mood

from the verb dormire = to sleep.

So dormit means:

• he sleeps
• she sleeps
• it sleeps

In this sentence, because the subject is puer, it means the boy sleeps.

Because its subject, puer, is singular.

In Latin, the verb agrees with its subject in person and number. Since puer is one boy, the verbs are singular:

• dormit = he sleeps
• audit = he hears

If the subject were plural, the verbs would also be plural. For example:

• pueri peius dormiunt, quia tonitrum audiunt
  The boys sleep worse because they hear thunder.

Tonitrum is accusative singular, because it is the direct object of audit.

He hears what?
He hears thunder.

That makes tonitrum the thing being heard, so it takes the accusative.

A helpful point: tonitrum is a neuter 2nd-declension noun, and in many neuter nouns the nominative and accusative singular look the same. So here:

• nominative singular: tonitrum
• accusative singular: tonitrum

Same form, different function.

Quia means because and introduces a causal clause.

So the sentence divides like this:

• Puer peius dormit = The boy sleeps worse
• quia tonitrum audit = because he hears thunder

In basic Latin, quia is a very common way to express cause or reason.

Because this sentence states a straightforward fact or reason: because he hears thunder.

Latin commonly uses the indicative after quia when the reason is presented as an actual fact. So:

• audit = present indicative, he hears

In more advanced Latin, especially in some authors, other constructions can appear depending on nuance, but for a learner this sentence is very normal and direct.

Yes. Latin word order is flexible, because the endings usually show what each word is doing.

This sentence is written in a perfectly normal order:

• Puer peius dormit, quia tonitrum audit.

But Latin could also rearrange it, for example:

• Quia tonitrum audit, puer peius dormit.
• Puer, quia tonitrum audit, peius dormit.

These all mean roughly the same thing. The differences are mostly in emphasis or style, not in core meaning.

Because the verb ending already tells you the subject.

Audit means he/she/it hears, and here the context makes it clear that it is the boy who hears. Latin often leaves out subject pronouns unless they are needed for emphasis or contrast.

So Latin can simply say:

• tonitrum audit = he hears thunder

without adding a separate word for he.

It can cover both ideas depending on context.

Tonitrum refers to the sound of thunder and can also suggest a peal or clap of thunder. In a sentence like this, English may translate it as:

• thunder
• the thunder
• a thunderclap

Any of these can fit the Latin sense, depending on how natural you want the English to sound.