Hún er komin í vinnuna, en hún kemst ekki inn af því að hún gleymdi kortinu sínu.

Hún er komin is a very common Icelandic way to say that someone has arrived and is now in the resulting state.

So:

• Hún kom í vinnuna = She came to work / She arrived at work (focus on the event)
• Hún er komin í vinnuna = She has arrived at work / She is at work now (focus on the result)

With verbs of motion, Icelandic often uses vera + past participle this way.

Because komin agrees with hún, which is feminine singular.

The participle changes for gender and number:

• hann er kominn = he has arrived
• hún er komin = she has arrived
• það er komið = it has arrived
• þeir eru komnir = they (masc.) have arrived
• þær eru komnar = they (fem.) have arrived

So the ending tells you something about the subject.

Because í takes different cases depending on meaning:

• accusative for motion/destination
• dative for location

Here the idea is arrival to work, so the destination is meant:

• í vinnuna = to work / to the workplace

If you were describing location, you would use:

• í vinnunni = in/at the workplace

So the contrast is roughly:

• Hún er komin í vinnuna = She has arrived at work
• Hún er í vinnunni = She is at work

Both patterns can occur in Icelandic, but they are not always felt exactly the same.

• í vinnuna often points to the workplace as a specific destination
• í vinnu can be more general, like to work as an activity or state

In this sentence, í vinnuna sounds very natural because she has arrived at a particular place: her workplace.

Kemst is from the verb komast, not from koma.

That is important:

• koma = come
• komast = get somewhere, manage to get somewhere, gain access, make it

So:

• hún kemst ekki inn = she can’t get in
• not just she doesn’t come in

It suggests that something prevents her from entering.

Inn means in / inside and works as a directional adverb.

Together, komast inn means:

• get in
• get inside
• gain entry

This is very common in Icelandic. Motion verbs often combine with words like:

• inn = in
• út = out
• upp = up
• niður = down

So kemst ekki inn is a natural fixed idea: can’t get in.

It means because.

You should learn it as a set phrase. It introduces the reason:

• af því að hún gleymdi kortinu sínu = because she forgot her card

Other ways to say because include:

• því að
• vegna þess að

But af því að is extremely common and natural.

Because the verb gleyma takes the dative case.

That means the thing forgotten is not in the accusative; it must be dative:

• kortið = the card (nom./acc.)
• kortinu = the card (dat.)

So:

• hún gleymdi kortinu = she forgot the card

This is one of those verbs where you need to learn the verb together with the case it requires.

Because sínu has to agree with kortinu, and kortinu is:

• neuter
• singular
• dative

The reflexive possessive sinn changes form depending on the noun it belongs to:

• sitt = neuter singular nominative/accusative
• sínu = neuter singular dative

Since kortinu is dative, sínu is the correct form:

• kortinu sínu = her own card

Because Icelandic normally uses reflexive possessives when the possessor is the subject of the same clause.

Here, in the clause hún gleymdi kortinu sínu, the subject is hún, and the card belongs to that same person. So Icelandic uses sinn:

• hún gleymdi kortinu sínu = she forgot her own card

If you said kortinu hennar, it would usually mean her card referring to some other female person, not the subject of the clause.

So this is an important distinction:

• sínu = her own
• hennar = hers / belonging to another woman or girl

Because each clause normally needs its own subject in Icelandic.

The sentence has three clauses:

• Hún er komin í vinnuna
• en hún kemst ekki inn
• af því að hún gleymdi kortinu sínu

Even though it is the same person each time, Icelandic normally repeats the pronoun. Unlike in some languages, you usually do not leave it out just because it was already mentioned.

Yes, but it is fairly standard Icelandic word order.

In the main clauses, the subject comes first:

• Hún er komin í vinnuna
• hún kemst ekki inn

After af því að, you get a subordinate clause:

• að hún gleymdi kortinu sínu

That is why the order is simply hún gleymdi, not something like gleymdi hún.

So the sentence shows a useful contrast:

• normal main clause order
• normal subordinate clause order after af því að