Skósmiðurinn sagði að hællinn á skónum mínum væri laus.

It is a compound noun:

• skó- = shoe
• smiður = smith, maker, craftsman

So skósmiður is literally something like shoe-maker / shoe-smith, i.e. shoemaker or cobbler.

The ending -inn is the suffixed definite article, so:

• skósmiður = a shoemaker
• skósmiðurinn = the shoemaker

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like English the.

Examples from the sentence:

• skósmiðurinn = skósmiður
  • -inn = the shoemaker
• hællinn = hæll
  • -inn = the heel
• skónum is the dative plural definite form of skór

So with skór:

• skóm = to/on shoes
• skónum = to/on the shoes

In Icelandic, this attached article is completely normal and extremely common.

Sagði is the past tense of segja, which means to say.

So:

• segja = to say
• segir = says
• sagði = said

This is not a fully regular-looking past tense, so it is a form learners usually just memorize.

In the sentence, it is 3rd person singular past because the subject is skósmiðurinn.

Here að is a conjunction meaning that.

It introduces the clause reporting what the shoemaker said:

• Skósmiðurinn sagði að ...
• The shoemaker said that ...

This is not the infinitive marker að used in forms like að vera = to be. Icelandic uses the same word for both jobs, so you have to tell from context.

Væri is the past subjunctive of vera (to be).

It is very commonly used in reported speech or indirect speech after verbs like segja. In other words, it marks the content as something someone said, rather than presenting it as a plain direct statement by the narrator.

So:

• er = is
• var = was
• væri = were / was, in a subjunctive-reported-speech sense

A useful way to think about it:

• ... að hællinn væri laus = the shoemaker said the heel was loose
• the speaker is reporting his statement

If you used var, that would sound more like the narrator is simply stating the fact more directly. The sentence with væri is the more textbook-like indirect-speech version.

Because the preposition á changes case depending on meaning:

• accusative = motion onto something
• dative = location on something

Here the heel is not moving onto the shoes; it is located on them. So Icelandic uses the dative.

That gives:

• skór = shoe
• skónum = on the shoes / on my shoes

And the possessive adjective has to match that form:

• mínum = dative plural

So:

• á skónum mínum = on my shoes

This dative-after-á for location is a very common Icelandic pattern.

In Icelandic, the most neutral, everyday pattern is often:

• noun first
• possessive after it

So:

• skónum mínum = my shoes
• bíllinn minn = my car
• bókin mín = my book

The possessive must agree with the noun it belongs to, not with the owner. Here it agrees with skónum, which is:

• masculine
• plural
• dative

So the correct form is mínum.

Also, when the possessive comes after the noun, the noun is usually definite:

• skónum mínum = my shoes

If you put the possessive before the noun, that is possible, but it is usually more emphatic or contrastive:

• mínum skóm

That would feel more like my shoes as opposed to someone else’s.

The whole subject is:

hællinn á skónum mínum

That entire phrase means the heel in question.

Inside it:

• hællinn = the heel
• á skónum mínum = on my shoes

So á skónum mínum is modifying hællinn. It tells you which heel we are talking about.

Then the rest is the predicate:

• væri laus = was loose / were loose

So the structure is basically:

• [subject] hællinn á skónum mínum
• [verb] væri
• [complement] laus

Because it agrees with hællinn.

Here laus is a predicate adjective after vera. Predicate adjectives in Icelandic agree with the subject in:

• gender
• number
• case

Hællinn is:

• masculine
• singular
• nominative

So the adjective appears as laus.

Compare:

• hællinn væri laus = the heel was loose
• hælarnir væru lausir = the heels were loose

So the form changes when the noun it describes changes.

A learner would usually look these up under the following dictionary forms:

• hællinn → hæll = heel
• skónum → skór = shoe
• mínum → minn = my
• væri → vera = to be
• laus → laus = loose

This is useful because Icelandic words often appear in heavily inflected forms in real sentences, so learning to identify the dictionary form is an important skill.