Það hangir stórt plakat um hátíðina í glugganum á kaffihúsinu.

Here Það does not mean a specific it. It is a dummy subject, much like English there in There is a big poster...

So:

• Það hangir ... = There is ... hanging ...
• not It hangs ... about some previously mentioned thing

This is a very common Icelandic pattern when introducing the existence of something.

Because the sentence uses the existential pattern with dummy það:

• Það hangir stórt plakat ...

This is similar to English:

• There hangs a big poster ...
• more naturally: There is a big poster hanging ...

The real thing being talked about is stórt plakat, but Icelandic often puts the verb right after það in this kind of sentence.

You could also make a more ordinary sentence like:

• Stórt plakat hangir í glugganum ...
• A big poster is hanging in the window ...

That version feels less like “introducing” the poster and more like simply describing it.

Hangir is the 3rd person singular present tense of hanga (to hang).

So it means:

• hangs
• or in more natural English here, is hanging

It is singular because the subject is stórt plakat (a big poster), which is singular.

Because plakat is a neuter singular noun in the nominative, and the adjective has to agree with it.

Agreement in Icelandic means the adjective matches the noun in:

• gender
• number
• case

Here:

• plakat = neuter
• singular
• nominative

So:

• stórt plakat = a big poster

The -t on stórt is the neuter singular nominative/accusative ending of the adjective.

It is the thing that is doing the “hanging,” so it is the grammatical subject.

In this sentence:

• Það is only a dummy subject
• stórt plakat is the real subject

You can also see this from the verb:

• hangir is singular
• plakat is singular

If the poster were plural, the verb would also be plural.

Um often takes the accusative case when it means about/concerning.

So:

• hátíð = festival (base form)
• hátíðina = the festival in the accusative singular

Thus:

• um hátíðina = about the festival

This phrase describes what the poster is about.

In Icelandic, the definite article is usually attached to the end of the noun.

So instead of a separate word like English the, Icelandic often uses an ending:

• hátíð = festival
• hátíðin = the festival (nominative)
• hátíðina = the festival (accusative)

The exact ending changes depending on case and number.

The same thing happens in:

• glugganum = the window
• kaffihúsinu = the café

Because í can take different cases depending on meaning:

• accusative for motion into something
• dative for location in something

Here the poster is already located there, not moving there, so Icelandic uses the dative:

• í glugganum = in the window

Compare:

• Ég set plakatið í gluggann. = I put the poster into the window.
  (motion → accusative)
• Plakatið hangir í glugganum. = The poster is hanging in the window.
  (location → dative)

Here á means something like at/on.

So:

• kaffihúsinu = the café (dative singular)
• á kaffihúsinu = at the café

In the full phrase:

• í glugganum á kaffihúsinu

the meaning is:

• in the window of the café
• more literally, in the window at the café

This is a very natural way in Icelandic to identify which window is meant.

Because both are controlled by prepositions expressing location.

• í glugganum: í
  • dative for location
• á kaffihúsinu: á
  • dative for location

So each preposition governs its own noun phrase.

This is one of the big things Icelandic learners need to get used to: prepositions often require a specific case, and some of them switch case depending on motion vs. location.

Icelandic has no indefinite article. There is no separate word for a/an.

So:

• plakat can mean poster or a poster
• stórt plakat = a big poster

Whether English uses a/an, the, or no article at all depends on context when translating.

It describes the poster.

So the structure is basically:

• Það hangir [stórt plakat um hátíðina] [í glugganum á kaffihúsinu].

That means:

• a big poster about the festival
• hanging in the café window

So um hátíðina tells you what kind of poster it is, while í glugganum á kaffihúsinu tells you where it is.

Yes, Icelandic word order is somewhat flexible, though some versions are more natural than others depending on focus.

For example, you could also say:

• Stórt plakat um hátíðina hangir í glugganum á kaffihúsinu.

This is more like a straightforward statement:
A big poster about the festival is hanging in the café window.

The original version with Það hangir ... is especially natural when introducing something as existing or present somewhere.

Both are possible.

Word-for-word, hangir is present tense:

• hangs

But in natural English, this sentence is often translated as:

• There is a big poster about the festival hanging in the café window.
• or A big poster about the festival is hanging in the café window.

So is hanging is often the most natural English equivalent here, even though Icelandic uses a simple present form.

They are:

• það = dummy subject / it, there
• hanga = to hang
• stór = big
• plakat = poster
• um = about
• hátíð = festival
• í = in
• gluggi = window
• á = on, at
• kaffihús = café, coffeehouse

This is useful because many words appear in changed forms in the sentence:

• hangir from hanga
• stórt from stór
• hátíðina from hátíð
• glugganum from gluggi
• kaffihúsinu from kaffihús