Hornhlífin er á borðinu.

The ending -in is the definite article attached to the noun, so it means the.

• hornhlíf = the basic noun
• hornhlífin = the hornhlíf

In Icelandic, the is very often added to the end of the noun instead of being a separate word like in English.

In this sentence, hornhlífin is:

• singular
• definite
• nominative
• feminine

So a learner should get used to seeing definiteness built into the noun itself.

Yes. Icelandic very often writes compound nouns as one word.

Here, hornhlíf is a compound:

• horn
• hlíf

That is very normal in Icelandic. English sometimes writes similar things as two words, one word, or hyphenated words, but Icelandic strongly prefers writing compounds together as a single word.

So hornhlífin is:

• the compound noun hornhlíf
• plus the definite ending -in

Because after á in the sense of location—being on something—Icelandic normally uses the dative case.

The basic noun is:

• borð = table

But in this sentence it becomes:

• borðinu = the table in the dative singular definite

So the structure is:

• á borðinu = on the table

This is a very important pattern:

• á
  • dative for location
• á
  • accusative for movement onto something

So:

• á borðinu = on the table, already there
• á borðið = onto the table, movement toward it

Because the sentence describes a static location, not movement.

A useful rule for Icelandic prepositions is:

• dative = location / position
• accusative = motion toward / change of place

So here:

• Hornhlífin er á borðinu = the object is on the table

But if you were saying that someone put it onto the table, you would expect the accusative:

• setti hana á borðið = put it onto the table

This location-vs-motion contrast is one of the most important things to notice in Icelandic case usage.

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

In this sentence:

• Hornhlífin er á borðinu
• literally: The hornhlíf is on the table

A useful thing to notice is that er is used with a third-person singular subject:

• hann er = he is
• hún er = she is
• það er = it is

So even though hornhlífin is feminine, the verb form is still just er. The verb does not change here according to grammatical gender.

There are two main clues:

1. It is in the nominative case, which is the normal case for the subject.
2. It comes before the verb in the basic statement word order.

So the sentence follows the very common pattern:

• subject + verb + prepositional phrase

That gives:

• Hornhlífin = subject
• er = verb
• á borðinu = where it is

This is the most neutral, straightforward word order in Icelandic.

Yes. Icelandic word order is more flexible than English word order.

For example, you could also say:

• Á borðinu er hornhlífin

That can sound more marked or more focused on the location.

But the version you were given:

• Hornhlífin er á borðinu

is the most natural basic order for a simple statement.

So for a learner, this sentence is a good example of the default pattern:

• subject first
• then verb
• then place expression

Very often, yes.

In ordinary Icelandic, the definite article is usually a suffix attached to the noun:

• borð = table
• borðið / borðinu = the table, depending on case

Likewise:

• hornhlíf = hornhlíf
• hornhlífin = the hornhlíf

There is also a separate form hinn/hin/hið, but that is not the normal everyday way to say the in a simple sentence like this. In most basic sentences, learners will most often see definiteness shown by the ending on the noun.

In this sentence:

• hornhlíf is feminine
• borð is neuter

That matters because gender affects:

• article endings
• adjective endings
• some case forms

For example:

• hornhlífin shows a feminine definite form
• borðinu shows a neuter dative definite form

So even in a short sentence like this, Icelandic is giving you information about both gender and case through the noun endings.

A few parts may stand out to an English speaker:

• á is not a plain English a; it has its own vowel sound.
• í is a long ee-like sound.
• ð in borðinu is like the th in this.
• hl in hlíf is a consonant combination English does not normally use at the start of a syllable.

So even if you already understand the meaning, this sentence is useful pronunciation practice because it includes several very Icelandic-looking sounds and spellings.

It would become:

• Hornhlíf er á borði

That means something like a hornhlíf is on a table or hornhlíf is on table, depending on context.

Here is the comparison:

• hornhlífin = the hornhlíf
• hornhlíf = a hornhlíf / hornhlíf in a general sense

and

• borðinu = the table
• borði = a table, in the dative singular

This is a good way to see how much information Icelandic packs into endings.