Hún er búin að fylla út eyðublaðið.

This is the very common Icelandic pattern:

vera + búinn/búin/búið + að + infinitive

It means that someone has finished doing something or is done with an action.

So here:

• hún er = she is
• búin að = finished with / done with
• fylla út eyðublaðið = fill out the form

A good way to think of it is that Icelandic is describing her current state: she is now in the state of having completed that action.

Because búinn is an adjective, and in Icelandic adjectives agree with the subject in gender and number.

Here the subject is hún, which is feminine singular, so the form is búin.

Compare:

• Hún er búin að... = she is finished doing...
• Hann er búinn að... = he is finished doing...
• Það er búið að... = it is finished / done...
• Þær eru búnar að... = they (feminine) are finished doing...

This agreement is very important and is one of the first things English speakers notice, because English does not change finished this way.

Because the sentence is talking about a present result or current state.

In other words, it does not literally focus on the past event itself. It focuses on the fact that right now she is done.

That is why Icelandic uses er = is.

This is similar to English ideas like:

• She is done filling out the form
• She has filled out the form

The Icelandic construction often overlaps in meaning with the English present perfect, but grammatically it is built differently.

Because after búin in this construction, Icelandic normally uses að + infinitive.

So:

• búin að fylla út = finished filling out / finished with filling out

The að here is the normal infinitive marker, like to in English, although in English we would not usually say she is finished to fill out the form. So the Icelandic structure does not map word-for-word onto English.

A useful chunk to memorize is:

• vera búin að gera eitthvað = to have finished doing something

Yes. Fylla út is a verb phrase that means to fill out.

• fylla by itself means fill
• út adds the sense of out, so together fylla út means fill out, especially for things like forms

So you should learn it as a unit:

• fylla út eyðublað = fill out a form

This is similar to English phrasal verbs, where the small extra word is an important part of the meaning.

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

So:

• eyðublað = form
• eyðublaðið = the form

The ending -ið is the definite article here.

This is extremely common in Icelandic:

• hús = house
• húsið = the house

So eyðublaðið is not a strange long word made from nowhere; it is simply eyðublað + the.

It is the direct object of fylla út, so it is in the accusative.

However, there is a detail that can confuse learners: for many neuter singular nouns, the nominative and accusative look the same.

So here:

• nominative singular: eyðublaðið
• accusative singular: eyðublaðið

That means the case is there grammatically, but you do not see a different ending in this particular word form.

They are very close in meaning, but not exactly the same in feel.

• Hún hefur fyllt út eyðublaðið = she has filled out the form
• Hún er búin að fylla út eyðublaðið = she is done filling out the form / she has finished filling out the form

A useful distinction is:

• hefur fyllt út is the regular perfect
• er búin að fylla út strongly emphasizes completion

In everyday Icelandic, vera búinn að is extremely common and often sounds very natural when the important idea is that the action is completed.

Yes, and this is a very important point.

Even with ég = I, the adjective still agrees with the speaker’s gender.

So:

• said by a man: Ég er búinn að fylla út eyðublaðið.
• said by a woman: Ég er búin að fylla út eyðublaðið.

This often feels unusual to English speakers, because English I am finished does not change based on the speaker’s gender. But in Icelandic, adjective agreement still happens.

You put ekki after the finite verb:

Hún er ekki búin að fylla út eyðublaðið.

That means She has not finished filling out the form or She is not done filling out the form.

So the pattern is:

• Hún er búin að... = She is finished...
• Hún er ekki búin að... = She is not finished...

In a yes/no question, the finite verb comes first:

Er hún búin að fylla út eyðublaðið?

That means Has she filled out the form? or Is she done filling out the form?

This verb-first pattern is very common in Icelandic yes/no questions.

Compare:

• Hún er búin að fylla út eyðublaðið. = statement
• Er hún búin að fylla út eyðublaðið? = question

The dictionary form is búinn.

That is the masculine singular nominative form, which is the form dictionaries normally list for adjectives.

So when you look it up, you would expect to find búinn, even though the sentence uses búin because the subject is feminine.

This is a good habit in Icelandic:

• if you see an adjective in context, remember that the dictionary entry is usually the masculine singular nominative form

Yes. Then you would usually drop the definite ending.

• eyðublað = a form
• eyðublaðið = the form

So:

• Hún er búin að fylla út eyðublað. = She has finished filling out a form.
• Hún er búin að fylla út eyðublaðið. = She has finished filling out the form.

This distinction is built directly into the noun form, not usually with a separate word like English the.