Ef ég hefði skilið beyginguna betur í gær, hefði ég ekki gert sömu villuna í dag.

It is a past counterfactual conditional.

That means the speaker is talking about something unreal: a different past situation and its imagined result. In other words, the sentence implies:

• I did not understand the inflection well enough yesterday.
• Because of that, I did make the same mistake today.

So Ef ég hefði skilið ... hefði ég ekki gert ... is the Icelandic way of expressing If I had understood ..., I would not have made ...

Hefði is the past subjunctive form of hafa (to have).

In this sentence, it is being used as an auxiliary verb together with a past participle:

• hefði skilið = had understood
• hefði gert = would have done / would have made

So hefði is a key signal that the sentence is hypothetical or contrary to fact.

This is a very common question for English speakers, because English and Icelandic do not match perfectly here.

In English, we usually say:

• If I had understood ...
• ... I would not have made ...

But in Icelandic, a past unreal conditional often uses hefði + past participle in both clauses:

• Ef ég hefði skilið ...
• hefði ég ekki gert ...

So even though English switches from had to would have, Icelandic can keep hefði in both parts.

This is because of Icelandic V2 word order in main clauses.

The opening Ef clause counts as the first element of the sentence:

• Ef ég hefði skilið beyginguna betur í gær, ...

After that, the main clause begins, and in Icelandic main clauses the finite verb usually comes next. So you get:

• hefði ég ekki gert sömu villuna í dag

If the main clause stood by itself, it would normally be:

• Ég hefði ekki gert sömu villuna í dag

So the fronted if clause causes the inversion.

They are past participles:

• skilið comes from skilja (to understand)
• gert comes from gera (to do, make)

With hafa or hefði, Icelandic uses the past participle to form perfect-type meanings:

• hef skilið = have understood
• hefði skilið = had understood
• hef gert = have done / have made
• hefði gert = would have done / would have made

A useful thing to notice is that these participles do not change here to agree with ég.

Because betur is an adverb, while betri is an adjective.

Here it modifies the verb skilið:

• skilið betur = understood better

You would use betri to describe a noun:

• betri bók = a better book
• betri nemandi = a better student

So:

• Ég skildi þetta betur = I understood this better
• not Ég skildi þetta betri

Beyginguna is the accusative singular definite form of beyging.

That happens because it is the direct object of skilja:

• skilja eitthvað = to understand something

So the sentence has:

• skilið beyginguna = understood the inflection

The pieces are roughly:

• beyging = inflection
• beygingu = inflection (accusative singular)
• beyginguna = the inflection

The definite article is attached to the end of the noun, which is very normal in Icelandic.

In grammar, beyging means inflection.

Depending on context, that can include things like:

• noun declension
• verb conjugation
• case endings
• person/number endings
• other word-form changes

So in this sentence, beyginguna probably means something like the inflection pattern or the grammatical endings/forms the speaker was trying to understand.

Because sömu has to agree with villuna.

Here, villuna is:

• feminine
• singular
• accusative
• definite

The adjective sami (same) is somewhat irregular, and in this context the correct form is sömu:

• sömu villuna = the same mistake

So the important thing to remember is that same in Icelandic changes form to match the noun, and sömu is the right form here.

In clauses like this, ekki usually comes before the past participle and other non-finite verb forms.

So:

• hefði ég ekki gert = would I not have made

The order is:

• finite verb: hefði
• subject: ég
• negation: ekki
• participle: gert

That is a very normal Icelandic pattern.

Yes. You can also say:

Ég hefði ekki gert sömu villuna í dag ef ég hefði skilið beyginguna betur í gær.

That means the same thing.

The main difference is word order:

• when the if clause comes first, you get hefði ég
• when the main clause comes first, you get ég hefði

So both are correct; the choice is mostly about sentence structure and emphasis.

These are fixed Icelandic time expressions:

• í gær = yesterday
• í dag = today

You should not try to translate the í too literally here. It is just part of the normal Icelandic expression.

So even though í often means in, in these phrases you simply learn them as whole units:

• í dag = today
• í gær = yesterday