Það er ekki mögulegt að fara út í dag.

Það often works like English it in sentences such as It is possible..., It is raining, or It is important....

In this sentence, það does not refer to a specific thing. It is a dummy subject or formal subject used because Icelandic, like English, usually wants a subject in the sentence.

So Það er ekki mögulegt... is structurally like It is not possible...

Er is the present tense singular form of the verb vera, meaning to be.

So:

• vera = to be
• er = is

That is why Það er... means It is...

Ekki means not.

In a basic Icelandic main clause, the finite verb usually comes early in the sentence, and ekki commonly follows it. So:

• Það er ekki mögulegt...
• literally: It is not possible...

This placement is very normal in Icelandic.

Compare:

• Hann kemur ekki. = He is not coming / He does not come.
• Þetta er ekki rétt. = This is not right.

Mögulegt is the neuter singular form of the adjective mögulegur meaning possible.

The three basic singular forms are:

• mögulegur = masculine
• möguleg = feminine
• mögulegt = neuter

Here Icelandic uses the neuter form because the adjective is describing the idea expressed by the clause að fara út í dag, and with það used as a formal subject, neuter singular is the normal choice.

A useful comparison:

• Ferðin er möguleg. = The trip is possible.
  Here ferðin is feminine, so möguleg is used.
• Það er mögulegt að fara. = It is possible to go.
  Here the neuter form mögulegt is used.

Here að is the infinitive marker, like English to in to go.

So:

• að fara = to go
• að borða = to eat
• að lesa = to read

In this sentence, mögulegt að fara means possible to go.

Be aware that að can also be a preposition in other contexts, but here it is simply marking the infinitive.

Fara is the infinitive form of the verb, meaning to go.

Because it follows the infinitive marker að, it stays in the infinitive:

• að fara = to go

You are not seeing a tense here. The tense of the whole sentence is carried by er:

• Það er ekki mögulegt... = It is not possible...
• að fara út í dag = to go out today

So the sentence is literally built as It is not possible to go out today.

Út means out or outside.

With fara, it forms a very common expression:

• fara út = go out / go outside

So the phrase að fara út means to go out.

In many cases, Icelandic uses short adverbs like this after verbs of movement:

• fara inn = go in
• fara út = go out
• koma heim = come home

Í dag means today.

Literally, it is made of:

• í = in
• dag = day

So historically it is something like in the day, but as a fixed expression it simply means today.

This is a very common Icelandic time expression.

The dictionary form is dagur meaning day, but after the preposition í in this expression, the noun appears in a different case.

In í dag, dag is the form used in this fixed adverbial phrase.

For a learner, the most practical thing is to remember í dag as a complete chunk meaning today.

Yes, to some extent. Icelandic allows more flexibility than English, especially for emphasis.

For example, you could say:

• Í dag er ekki mögulegt að fara út.

This puts extra focus on today.

However, Icelandic still follows important word-order rules, especially the tendency for the finite verb to appear early in main clauses. So not every rearrangement will sound natural.

The original sentence is a very neutral, standard way to say it.

Yes. A very common alternative would be:

• Það er ómögulegt að fara út í dag.

Here ómögulegt means impossible, which is stronger than ekki mögulegt meaning not possible.

So:

• ekki mögulegt = not possible
• ómögulegt = impossible

Both are correct, but the nuance is slightly different.

A rough pronunciation guide could be:

• Það ≈ thahth
• er ≈ ehr
• ekki ≈ ehk-ih
• mögulegt ≈ MEU-gu-lekht
• að ≈ ahth
• fara ≈ FA-ra
• út ≈ oot
• í dag ≈ ee dahk

A few important sounds for English speakers:

• þ is like th in thing
• ð is like th in this, though at the end of a word it can sound weaker
• ö is a rounded vowel that does not exist exactly in English
• g in some Icelandic words can sound softer than English g

This is only approximate, but it can help you get started.