Brúðkaupið er á morgun.

Brúðkaup means a wedding (indefinite).

In Icelandic, the definite article (the) is usually attached to the end of the noun instead of being a separate word in front, like in English.

• brúðkaup = a wedding
• brúðkaupið = the wedding

The ending -ið is the neuter singular definite ending in the nominative case.
So brúðkaupið literally means “the wedding”.

Brúðkaup is a neuter noun.

For neuter nouns in the nominative singular:

• Indefinite form: just the base word
  
  • brúðkaup (a wedding)
• Definite form: add -ið
  
  • brúðkaupið (the wedding)

So the fact that brúðkaup is neuter is exactly why the definite ending is -ið and not something like -inn or -in.

Icelandic does not normally use a separate word before nouns for “the”.
Instead, the definite article is a suffix:

• masculine: -inn (e.g. stóll → stóllinn = the chair)
• feminine: -in (e.g. bók → bókin = the book)
• neuter: -ið (e.g. brúðkaup → brúðkaupið = the wedding)

So brúðkaupið already includes the meaning “the wedding”; there is no separate word needed.

Yes. Er is the 3rd person singular present tense of the verb að vera (to be).

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Here, the subject is brúðkaupið (the wedding), which is 3rd person singular, so you use er:

• Brúðkaupið er á morgun.
  The wedding is tomorrow.

Icelandic very often uses the present tense to talk about the near future, especially for scheduled events, plans, and arrangements.

So:

• Brúðkaupið er á morgun.
  literally: The wedding is tomorrow,
  but in context: The wedding is (going to be) tomorrow.

This works much like English sentences such as:

• The concert is tomorrow.
• The flight is at 9 a.m.

You can also say Brúðkaupið verður á morgun (the wedding will be tomorrow) using verður (will be), but er is completely natural here.

Á morgun is a very common phrase meaning tomorrow.

Literally:

• á = on / at (here, used for time)
• morgun = morning (accusative/dative form of morgunn)

So literally it is something like “on (the) morning”, but idiomatically it just means “tomorrow”.

In time expressions like this, á often governs the accusative and is used similarly to English on / at:

• á morgun = tomorrow
• á mánudag = on Monday
• á þriðjudaginn = on Tuesday

In practice, you just learn á morgun as the fixed way to say tomorrow.

The noun is morgunn (morning), with these singular forms:

• Nominative: morgunn
• Accusative: morgun
• Dative: morgni
• Genitive: morguns

In á morgun, the preposition á is used for a time expression and takes the accusative:

• á morgun → accusative morgun

It doesn’t look different from the dative, because accusative and dative can coincide in some forms, but here it is best analysed as accusative due to the usual rule á + acc for time (“on Monday”, “on Friday”, etc.).

They mean different things:

• á morgun = tomorrow (in the future)

  • Brúðkaupið er á morgun.
    The wedding is tomorrow.

• í morgun = this morning / earlier today

  • Ég fór í vinnuna í morgun.
    I went to work this morning.

So for talking about the future day, you must use á morgun, not í morgun.

You can, but it changes the meaning.

• Brúðkaupið er á morgun.
  The wedding is tomorrow. (a specific, known wedding)

• Brúðkaup er á morgun.
  Literally: A wedding is tomorrow. / There’s a wedding tomorrow.
  (introducing the idea of some wedding, not previously specified)

In most real-life situations, if you and the listener both know which wedding you are talking about, you use the definite form: brúðkaupið.

Both word orders are possible and correct:

1. Brúðkaupið er á morgun.
2. Á morgun er brúðkaupið.

The basic neutral order is Subject – Verb – (other elements):

• Brúðkaupið (S) er (V) á morgun.

But Icelandic, like English, can move time expressions to the front for emphasis or to set the scene:

• Á morgun er brúðkaupið.
  Emphasis on “tomorrow” (e.g. contrasting with some other time).

Both are correct but have a slightly different feel:

• Brúðkaupið er á morgun.
  Neutral statement; like English “The wedding is tomorrow.”
  Present tense used for a scheduled future event.

• Brúðkaupið verður á morgun.
  Literally “The wedding will be tomorrow.”
  Slightly more focus on the occurrence or taking place of the event.

In everyday speech, er á morgun is extremely common and perfectly natural.

Approximate pronunciation (in a broad English-friendly way):

• brúðkaupið ≈ [BRUUTH-køy-pith]

More precisely:

• brúð – ú like oo in food; ð is a soft th as in this, often quite weak
• kaup – au is a diphthong, roughly like öy / oi; p is like English p
• ið – i like i in bit; ð again like a soft th in this

The cluster ðk is not pronounced as two strong separate consonants; the ð is often weakened or almost disappears before k, so it comes out closer to something like brúk- or brú-k to an English ear.