Bróðirinn er eldri en systirin.

Because Icelandic usually expresses the definite article as a suffix attached to the noun.

• bróðir = brother
• bróðirinn = the brother
• systir = sister
• systirin = the sister

So instead of a separate word like English the, Icelandic often adds -inn / -in / -ið or related forms to the noun itself.

Because when the definite article is added, the form of the noun can change slightly. These are normal Icelandic inflection patterns.

• bróðir → bróðirinn
• systir → systirin

This is not something you can always predict perfectly from English, so it is best to learn noun forms together with their gender and common case forms.

Er means is. It is the present tense, 3rd person singular form of the verb vera (to be).

So:

• Bróðirinn er ... = The brother is ...

This is one of the most common verbs in Icelandic, and like English to be, it is irregular.

Because eldri is the comparative form of the adjective meaning old in the sense of age.

The basic adjective is:

• gamall = old

But its comparative is irregular:

• eldri = older
• elstur = oldest

So Icelandic does not build this comparison in a simple regular way here. You just have to learn that gamall → eldri.

In this sentence, eldri is the correct comparative form for both masculine and feminine singular in this kind of use.

Here:

• bróðirinn is masculine
• systirin is feminine
• the comparison word stays eldri

So eldri works naturally here as older. If the subject were neuter, you might see eldra in some contexts.

Here en means than.

So:

• eldri en systirin = older than the sister

This is the normal word used in comparisons.

Be aware that en can also mean but in other sentences, but after a comparative adjective like eldri, it means than.

Because Icelandic often treats this type of comparison as if a whole clause were understood:

• Bróðirinn er eldri en systirin [er].
• The brother is older than the sister [is].

Since systirin is understood as the subject of the omitted verb er, it stays in the nominative.

That is different from what an English speaker might expect, because English does not show case very much here.

In a way, yes. You can think of it as an omitted repeated verb.

Fuller version:

• Bróðirinn er eldri en systirin er.

But Icelandic normally leaves the second er out because it is obvious.

So the actual sentence is completely natural and complete as written.

No, this is a very normal Icelandic sentence pattern:

• Subject: Bróðirinn
• Verb: er
• Complement: eldri en systirin

That is similar to basic English word order:

• The brother / is / older than the sister

So for an English speaker, the structure is fairly familiar.

Yes. That means The sister is younger than the brother, and it expresses the same relationship from the other side.

• Bróðirinn er eldri en systirin = The brother is older than the sister
• Systirin er yngri en bróðirinn = The sister is younger than the brother

Both are natural.

It is making a comparison.

The structure is:

• The brother is older than the sister

So it is not just naming him as the older brother. It is explicitly comparing the ages of the two people.

A rough learner-friendly approximation is:

• bróðirinn ≈ BROH-thi-rin

A few useful points:

• ó is a long vowel, roughly like o in go
• ð is like the th in this, not thin
• the final -inn is the definite article ending

The exact Icelandic pronunciation is more subtle, but that approximation is a good start.

Rough approximations:

• eldri ≈ EL-dri
• systirin ≈ SIS-ti-rin or SIS-ti-rin with an Icelandic y sound that is not exactly English i

A few notes:

• y in Icelandic is pronounced like i, even though it is written differently
• r is usually trilled or tapped more clearly than in most English accents
• unstressed endings are often lighter and quicker than English learners expect

You can, but it would not mean the same thing in the usual sense.

• Bróðirinn ... systirin = the brother ... the sister
  Specific people are being compared.
• Bróðir ... systir without the article sounds more general, less natural in this exact context, or dependent on a broader context.

So if you mean particular people, the definite forms are the right choice here.

In this sentence, eldri describes bróðirinn, the subject.

So the structure is:

• Bróðirinn = the person being described
• er eldri = is older
• en systirin = than the sister

The sister is only the standard of comparison, not the main noun being described.