Iudex furi poenam gravem dat, quia lex clara est.

Because iudex is in the nominative singular, which is the case normally used for the subject.

• iudex = judge
• Dictionary form: iudex, iudicis
• It is a 3rd-declension noun

Also, the verb dat is 3rd person singular (he/she/it gives), so it matches a single subject: iudex.

Furi is the dative singular of fur, furis (thief).

The dative often marks the indirect object, meaning the person to whom something is given:

• iudex furi poenam dat
  = the judge gives a punishment to the thief

In smoother English, we often say:

• the judge gives the thief a punishment
• or better, the judge inflicts a punishment on the thief

So furi answers the question to whom?

Because poenam is the direct object of dat.

It is the thing being given:

• poena = punishment, penalty
• poenam = accusative singular

So in the sentence:

• iudex = subject
• furi = indirect object
• poenam = direct object

A very literal layout is:

• The judge gives to the thief a punishment

Because gravem has to agree with poenam.

Gravis is the dictionary form of the adjective, meaning heavy, serious, or severe.
Here it describes poenam, so it must match it in:

• gender: feminine
• number: singular
• case: accusative

So:

• poenam = feminine singular accusative
• gravem = feminine singular accusative

That is why Latin uses gravem poenam or poenam gravem, not gravis poenam.

Yes, literally it does. But in Latin, poenam dare is a normal expression meaning:

• to inflict punishment
• to impose a penalty
• to punish

So although dat means gives, the whole phrase is more naturally understood as:

• The judge gives the thief a severe punishment
• or The judge inflicts a severe punishment on the thief

Dat is the 3rd person singular present active indicative of do, dare, meaning to give.

So:

• do = I give
• das = you give
• dat = he/she/it gives

Here it means:

• the judge gives

Because it is present tense, the sentence describes a present or general action.

Quia means because.

It introduces a causal clause:

• quia lex clara est
• because the law is clear

So the second part explains the reason for the first part.

Main clause:

• Iudex furi poenam gravem dat
• The judge gives the thief a severe punishment

Reason clause:

• quia lex clara est
• because the law is clear

Because clara is a predicate adjective, not a direct object.

After a form of to be (est), the adjective that describes the subject stays in the nominative, matching the subject:

• lex = nominative singular feminine
• clara = nominative singular feminine

So:

• lex clara est = the law is clear

If you used claram, that would be accusative, which would not fit here.

Latin word order is much more flexible than English word order because the endings show each word’s role.

English depends heavily on order:

• The judge punishes the thief is different from
• The thief punishes the judge

Latin can move words around more freely because the cases make the roles clear:

• iudex = subject
• furi = indirect object
• poenam = direct object

So Iudex furi poenam gravem dat is natural Latin, even though it is not in standard English order.

A common Latin tendency is to put the verb near the end, but this is not a strict rule.

Latin has no articles.

So a Latin noun can mean:

• a judge
• the judge

depending on context.

That means:

• iudex could be a judge or the judge
• lex could be a law or the law

English has to choose an article, but Latin often leaves that to the reader or context.

Yes. Latin allows both positions:

• poenam gravem
• gravem poenam

and

• lex clara
• clara lex

All of these are grammatically possible.

Often, adjective placement can create a slight difference in emphasis or style, but in a basic sentence like this, the core meaning stays the same.

So poenam gravem simply means a severe punishment, even though English usually puts the adjective first.

Yes:

• Iudex — nominative singular, 3rd declension noun; subject
• furi — dative singular of fur, furis; indirect object
• poenam — accusative singular of poena, poenae; direct object
• gravem — accusative singular feminine of gravis, grave; agrees with poenam
• dat — 3rd singular present active indicative of do, dare
• quia — conjunction meaning because
• lex — nominative singular of lex, legis; subject of the subordinate clause
• clara — nominative singular feminine of clarus, clara, clarum; agrees with lex
• est — 3rd singular present indicative of sum, esse; is

So the structure is:

• [Iudex] [furi] [poenam gravem] [dat]
• [quia] [lex] [clara] [est]

Not necessarily by grammar alone.

Since Latin has no articles, the sentence could mean:

• The judge gives the thief a severe punishment
• A judge gives a thief a severe punishment

Context usually tells you whether the people are specific or general.

In many textbook translations, English uses the because it sounds more natural.