Kennarinn segir að lýsingarorðið sé ekki rétt.

Because Icelandic usually puts the definite article on the end of the noun.

• kennari = teacher
• kennarinn = the teacher

So -inn here is the suffixed definite article.
In this sentence, Kennarinn is the subject of the main clause.

Segir is the 3rd person singular present tense of segja, meaning to say.

So:

• ég segi = I say
• þú segir = you say
• hann/hún/það segir = he/she/it says

Because Kennarinn is singular, the verb is singular too: Kennarinn segir.

Here að means that and introduces a subordinate clause.

So the structure is:

• Kennarinn segir = The teacher says
• að lýsingarorðið sé ekki rétt = that the adjective is not correct

A very common learner question is whether að always means the same thing. It does not:

• að can be the infinitive marker, like to
• að can also be a conjunction, like that

Here it is clearly the conjunction that, because it is followed by a full clause with its own subject and verb.

It is a compound noun plus the definite article.

Breakdown:

• lýsing = description
• orð = word
• lýsingarorð = adjective, literally something like describing word
• lýsingarorðið = the adjective

The ending -ið is the definite article for this neuter noun.

Compound words are extremely common in Icelandic, so getting used to breaking them apart is very helpful.

It is in the nominative singular.

Why? Because inside the subordinate clause, lýsingarorðið is the subject of sé.

So in:

• að lýsingarorðið sé ekki rétt

the subject is lýsingarorðið, and subjects are normally nominative.

Because segja is not directly taking lýsingarorðið as its object here.
Instead, the whole clause after að is what segir governs.

So the structure is:

• Main clause: Kennarinn segir
• Subordinate clause: að lýsingarorðið sé ekki rétt

You can think of the entire subordinate clause as the content of what the teacher says.

Sé is the present subjunctive of vera, meaning to be.

• er = indicative present
• sé = subjunctive present

In sentences of reported speech or reported opinion, Icelandic often uses the subjunctive in the subordinate clause, especially in more careful or formal language.

So:

• Kennarinn segir að lýsingarorðið sé ekki rétt

has the sense of reporting what the teacher says, rather than the speaker directly stating it as their own plain assertion.

Learners should especially remember this with verbs like:

• segja = say
• halda = think
• telja = consider

You may sometimes hear indicative forms in everyday speech, but sé is a very standard and important pattern to learn.

Because ekki negates the predicate here.

In this clause:

• sé ekki rétt = is not correct

the word order is natural Icelandic:

• verb: sé
• negation: ekki
• predicate adjective: rétt

So ekki comes before the adjective it is negating.

Because predicate adjectives in Icelandic agree with the noun they describe in gender, number, and usually case.

Here the noun is:

• lýsingarorðið
• neuter
• singular
• nominative

So the adjective must match that:

• réttur = masculine singular nominative
• rétt = neuter singular nominative
• rétt can also be feminine singular in some contexts, but here it is neuter because it matches lýsingarorðið

That is why the sentence has rétt, not réttur.

As a learner, it is best to keep it.

With segja, standard Icelandic normally uses að before a subordinate clause:

• Kennarinn segir að ...

In some informal spoken language, speakers may sometimes omit it, but that is not the safest pattern for learners. If you use að, your sentence will sound normal and correct.

Yes. The clause

• að lýsingarorðið sé ekki rétt

has a very normal order:

• conjunction: að
• subject: lýsingarorðið
• verb: sé
• negation: ekki
• predicate adjective: rétt

So this is a good model sentence for learning how reported clauses are built in Icelandic.