Asigurătorul îl despăgubește pe asigurat.

They come from the same insurance-related word family:

• a asigura = to insure / to assure
• asigurător = insurer
• asigurat = insured person

So:

• asigurătorul = the insurer
• asigurat = the insured / the insured person

A useful pattern to notice:

• -ător often makes an agent noun: the one who does the action
• -at often gives a result/passive idea: the one who is affected by the action

So the sentence sets up a very typical pair: the company/person providing insurance and the person covered by it.

Because Romanian usually puts the definite article at the end of the noun, not as a separate word before it.

So:

• asigurător = insurer
• asigurătorul = the insurer

This is one of the first big differences from English. Instead of the insurer, Romanian says something more like insurer-the.

The same pattern appears all over the language:

• băiat = boy
• băiatul = the boy
• client = client
• clientul = the client

Despăgubește is the 3rd person singular present tense of a despăgubi.

So it means:

• he/she/it compensates
• he/she/it indemnifies
• he/she/it reimburses for a loss, depending on context

In this sentence, the subject is asigurătorul, which is singular, so the verb is also singular:

• Asigurătorul despăgubește... = The insurer compensates...

In legal or insurance language, the Romanian present tense often expresses a general rule or standard action, not just something happening right now.

Yes, it does repeat the object in a way, and that is completely normal in Romanian.

• îl = him
• pe asigurat = the insured

Romanian very often uses a direct-object clitic pronoun together with a full direct object, especially when the object is:

• a person
• specific/identified
• introduced by pe

This is called clitic doubling.

So:

• îl despăgubește pe asigurat
  literally feels like
• compensates him, the insured

In English, that sounds redundant. In Romanian, it is natural grammar.

Here pe marks the direct object because the object is a person and is specific.

So in:

• îl despăgubește pe asigurat

pe asigurat is the person receiving the action.

This pe often appears with human direct objects in Romanian. It does not mean on here, even though pe can mean on in other contexts.

Compare the idea:

• văd omul = I see the man
• îl văd pe om = I see the man

With people, especially specific people, pe is very common and often expected.

This is a very good question, because it looks strange if you expect the full definite article every time.

After pe, especially with a masculine singular noun referring to a person or role, Romanian often uses the noun without the ending definite article when it stands alone:

• pe profesor
• pe doctor
• pe asigurat

This can still mean the professor / the doctor / the insured, depending on context.

If the noun is further specified, the full definite form is very common:

• pe asiguratul din contract = the insured person from the contract
• pe profesorul nou = the new professor

If you want an indefinite meaning, you would usually say:

• pe un asigurat = an insured person

So pe asigurat in your sentence is normal and idiomatic.

You may hear reduced versions in some contexts, but îl is the natural standard choice here.

With a specific human direct object introduced by pe, Romanian strongly prefers the clitic:

• Asigurătorul îl despăgubește pe asigurat.

That version sounds complete and idiomatic.

Without îl, the sentence may sound less natural or less standard, especially in careful written Romanian.

So for a learner, the safest model is:

• clitic + verb + pe + person

No, Romanian word order is fairly flexible, although some orders are more neutral than others.

The most neutral version here is:

• Asigurătorul îl despăgubește pe asigurat.

But you can move things around for emphasis:

• Pe asigurat îl despăgubește asigurătorul.
  This puts more focus on the insured.

• Asigurătorul pe asigurat îl despăgubește.
  Also possible, but more marked.

Because Romanian uses markers like îl and pe, the roles are still clear even when the order changes.

The main tricky letters are:

• ă in asigurătorul, despăgubește
  This is a short central vowel, somewhat like the a in sofa

• î in îl
  This is a sound English does not really have; keep it short and central

• ș in despăgubește
  This is sh

A rough learner-friendly guide:

• asigurătorul ≈ ah-see-goo-ruh-TOR-ul
• îl ≈ a very short central vowel + l
• despăgubește ≈ des-puh-goo-BESH-te
• asigurat ≈ ah-see-goo-RAT

The main stresses are:

• asigurătórul
• despăgubéște
• asigurát

In insurance language, all three can be possible depending on context, but compensates or indemnifies are usually the best matches.

• compensates = good general meaning
• indemnifies = especially good in legal/insurance contexts
• reimburses = sometimes possible, but often narrower in English

So in this sentence, the most natural legal-style understanding is:

• The insurer indemnifies the insured or
• The insurer compensates the insured

Most likely a general rule.

Romanian present tense often works like English present tense in definitions, rules, and legal statements. So this sentence usually means something like:

• this is what an insurer does
• this is the insurer’s obligation
• this is the standard relationship between the two parties

If you wanted to make it clearly about a completed past event, Romanian would use a past tense instead.