Cives ipsi iura sua servare volunt.

The sentence breaks down like this:

• cives = citizens; the subject
• ipsi = themselves or the very ...; adds emphasis to cives
• iura = rights/laws; the direct object
• sua = their own; modifies iura
• servare = to preserve / to keep / to observe
• volunt = they want

So the structure is:

• subject: cives ipsi
• object: iura sua
• verb phrase: servare volunt

Latin often puts the main finite verb at the end, so volunt comes last.

Because cives is nominative plural, the case normally used for the subject of a sentence.

The noun is from civis, civis and can mean citizen. Its nominative plural is cives.

You can also tell it is the subject because the verb volunt is plural: they want. That matches cives = citizens.

Ipsi is an intensive pronoun/adjective meaning something like:

• themselves
• the very citizens
• citizens themselves

It emphasizes the subject. So the idea is not just the citizens want..., but the citizens themselves want...

Here ipsi agrees with cives:

• masculine
• plural
• nominative

It does not act as a separate subject. It strengthens cives.

Because it agrees with cives, which is plural.

In Latin, words like ipse, ipsa, ipsum must match the noun they go with in:

• gender
• number
• case

Since cives here is masculine plural nominative, the matching form is ipsi.

Iura sua is accusative plural, because it is the direct object of servare.

The verb servare takes an object: you preserve, keep, or observe something.
That something here is iura sua = their own rights.

Details:

• iura is the accusative plural of ius
• sua agrees with iura, so it is also accusative plural neuter

Because iura is the plural of ius.

• ius = right, law, legal right
• iura = rights or sometimes laws/legal principles

This is a common neuter noun pattern in Latin:

• singular nominative/accusative: ius
• plural nominative/accusative: iura

Since iura is neuter plural, the adjective sua also appears in the neuter plural form.

Because sua is reflexive: it refers back to the subject of the clause.

Here the subject is cives, so sua means their own in the sense the citizens' own.

Compare:

• iura sua = their own rights; the rights belonging to the subject
• iura eorum = their rights; the rights of some other people, not necessarily the subject

So sua is exactly what Latin normally uses when possession points back to the subject.

Grammatically, sua agrees with iura, not with cives.

That means it matches iura in:

• case
• number
• gender

So it is neuter plural accusative because iura is neuter plural accusative.

However, in meaning, sua refers back to cives, the subject.
This is an important Latin idea:

• agreement is with the noun modified
• reference can point back to the subject

Because it depends on volunt.

Latin often uses a complementary infinitive after verbs like:

• volo = want
• possum = can
• debeo = ought
• soleo = am accustomed

So:

• volunt servare = they want to preserve

This is very similar to English want to preserve.

Because its subject, cives, is plural.

Volunt is the 3rd person plural present tense of velle:

• vult = he/she wants
• volunt = they want

Since cives means citizens, plural, the verb must also be plural.

Because Latin word order is much freer than English word order.

Putting the finite verb at the end is very common in Latin, especially in straightforward prose. So:

• Cives ipsi iura sua servare volunt

is a very natural Latin order.

Latin uses endings, not position alone, to show grammatical relationships. That is why the words can move around more freely.

This order also gives a nice progression:

• who? — cives ipsi
• what? — iura sua
• what do they want to do? — servare volunt

Yes. You could say:

• Cives iura sua servare volunt.

That would still mean The citizens want to preserve their own rights.

Adding ipsi makes the sentence more emphatic. It suggests something like:

• The citizens themselves want to preserve their own rights
• The citizens, on their own part, want to preserve their rights

So ipsi is not required for grammar, but it adds emphasis and tone.

Servare can mean several related things, depending on context:

• to preserve
• to keep
• to protect
• to observe (as in laws, rules, rights)

With iura, it can mean:

• preserve rights
• maintain rights
• uphold rights
• observe legal rights/laws

So the exact English wording may vary, but the Latin grammar stays the same.