Við göngum áfram, jafnvel þótt stígurinn sé blautur.

Because jafnvel þótt introduces a concessive clause, meaning something like even though / although. After þótt, Icelandic very often uses the subjunctive mood.

• sé = subjunctive form of að vera (to be)
• er = indicative form of að vera

So:

• stígurinn er blautur = the path is wet
• jafnvel þótt stígurinn sé blautur = even though the path is wet

For learners, the key pattern to remember is:

• þótt + subjunctive is very common

In everyday speech, you may sometimes hear indicative forms in some contexts, but sé is the standard and expected form here.

Jafnvel þótt means even though or even if, depending on context.

It is made up of:

• jafnvel = even
• þótt = though / although

Together they strengthen the contrast:

• þótt = although
• jafnvel þótt = even though

So the phrase signals: this fact does not stop the action in the main clause.

Göngum is the 1st person plural present tense of að ganga (to walk).

So:

• ég geng = I walk
• við göngum = we walk

In this sentence, Við göngum áfram means we keep walking / we walk on / we continue walking.

The verb ganga is a very common strong verb, so its forms change in ways that are not always fully predictable for beginners.

Because stígurinn means the path, while stígur means a path.

Icelandic usually adds the definite article to the end of the noun:

• stígur = a path
• stígurinn = the path

So the -inn ending here is the attached word for the.

Also, stígurinn is in the nominative singular, because it is the subject of the clause stígurinn sé blautur.

Because Icelandic adjectives must agree with the noun they describe in:

• gender
• number
• case

Here, stígurinn is:

• masculine
• singular
• nominative

So the adjective must also be masculine singular nominative:

• blautur = wet

Compare:

• blautur stígur = a wet path
• blauta stíginn = the wet path (accusative)
• blautt barn = a wet child/thing if neuter
• blaut gata = a wet street if feminine

So blautur matches stígurinn correctly.

Áfram means on, forward, or ahead. In this sentence, it gives the idea of continuing.

So:

• Við göngum áfram = We walk on
• Við höldum áfram = We continue

With motion verbs, áfram often means:

• moving onward
• continuing despite something
• not stopping

That is why it fits very naturally with the idea of even though the path is wet.

Yes. A very natural alternative is:

• Jafnvel þótt stígurinn sé blautur, göngum við áfram.

This means the same thing.

Notice what happens in the main clause after the subordinate clause comes first:

• Við göngum áfram
  becomes
• göngum við áfram

That is because Icelandic follows a verb-second pattern in main clauses. If the subordinate clause comes first, it takes the first position, and then the finite verb of the main clause comes next.

So both are correct:

• Við göngum áfram, jafnvel þótt stígurinn sé blautur.
• Jafnvel þótt stígurinn sé blautur, göngum við áfram.

They are related, but they are not used the same way.

• þó often means though, however, or still
• þótt is commonly used as a conjunction meaning although / though, and it often triggers the subjunctive

Examples:

• Það er kalt. Ég fer þó út.
  It is cold. I am going out anyway / though.

• Þótt það sé kalt, fer ég út.
  Although it is cold, I am going out.

In your sentence, þótt is the right form because it introduces a subordinate clause.

These are two Icelandic letters that English speakers usually ask about right away.

• þ is like th in thin
• ð is like th in this

In your sentence:

• þótt begins with þ → like th in thin
• Við contains ð → like th in this

A rough learner-friendly pronunciation guide for the whole sentence could be:

• Vith GURNG-um OY-frame, YINE-vel thott STEE-gur-in syeh BLUY-tur

That is only approximate, but the key point is:

• þ = voiceless th
• ð = voiced th

The comma separates the main clause from the subordinate concessive clause.

Main clause:

• Við göngum áfram

Subordinate clause:

• jafnvel þótt stígurinn sé blautur

In Icelandic, commas are commonly used to mark this kind of clause boundary, especially in clear written style. So the comma helps show the structure of the sentence.

The sentence has two parts:

1. Main clause: Við göngum áfram

   • Við = subject
   • göngum = verb
   • áfram = adverb

2. Subordinate concessive clause: jafnvel þótt stígurinn sé blautur

   • jafnvel þótt = even though
   • stígurinn = subject
   • sé = subjunctive verb
   • blautur = predicate adjective

So the overall pattern is:

• main clause + even though + subordinate clause

That makes it a very useful model sentence for learning:

• motion verb + áfram
• concessive clause with þótt
• subjunctive sé
• adjective agreement with a noun

Yes, sometimes the English translation can shift between even though and even if depending on context.

In this sentence, because the path actually seems to be wet, even though is the most natural translation.

But Icelandic jafnvel þótt can also be used in contexts where English prefers even if. The exact English choice depends on whether the speaker is talking about:

• a real fact → even though
• a hypothetical possibility → even if

So here:

• Við göngum áfram, jafnvel þótt stígurinn sé blautur. is most naturally understood as
  We keep walking, even though the path is wet.

But the Icelandic structure itself can cover both kinds of contrast depending on context.