Hún vill bara smá kaffi.

• Hún = she
• vill = wants
• bara = just / only
• smá = a little / some
• kaffi = coffee

So the sentence structure is:

subject + verb + adverb + object phrase

That is very normal Icelandic word order for a simple main clause.

Because vilja is the infinitive, meaning to want. In the sentence, the verb has to match hún = she, so Icelandic uses the 3rd person singular present form:

• ég vil = I want
• þú vilt = you want
• hann / hún / það vill = he / she / it wants

So hún vill means she wants.

Also, vilja is an irregular verb, so its forms are worth memorizing separately.

Hún is the 3rd person singular feminine pronoun, so it means she.

A learner may notice that Icelandic has three genders:

• masculine
• feminine
• neuter

When referring to a woman or girl, hún is the normal pronoun. In other contexts, pronouns can also follow the grammatical gender of nouns, not just natural gender.

In this sentence, though, it simply means she.

Here bara means just or only.

It limits the statement:

• she does not want a full meal
• she does not want something complicated
• she wants only a small amount of coffee

Bara is a very common Icelandic adverb, and its exact English translation depends on context:

• just
• only
• sometimes simply

In this sentence, just / only is the most natural idea.

Here smá is a very common everyday modifier meaning a little or some.

In this use, it is often treated as an indeclinable word, which means it does not change form for gender, number, or case the way many Icelandic adjectives do.

That is one reason learners notice it: Icelandic usually has lots of agreement, but smá often stays the same.

So in smá kaffi, you can think of it as meaning:

• a little coffee
• some coffee

You certainly may also meet lítið kaffi, because lítið is the regular neuter singular form of lítill = small / little.

But smá kaffi is extremely natural in everyday Icelandic and often sounds more idiomatic for a little coffee / some coffee.

A useful rough distinction is:

• smá kaffi = very common, conversational, natural
• lítið kaffi = also possible, but often feels a bit more literal or formal

So for ordinary spoken Icelandic, smá kaffi is a great phrase to learn.

Kaffi is the direct object of vill, so it is in the accusative case.

However, the form does not visibly change here. That is because kaffi is a neuter noun, and in the singular its nominative and accusative forms are the same:

• nominative: kaffi
• accusative: kaffi

So even though the case is accusative, the word still looks exactly the same.

In Icelandic, mass nouns such as coffee often appear without an article when you mean an indefinite amount.

So smá kaffi naturally means:

• some coffee
• a little coffee

If you wanted the coffee, Icelandic normally uses the suffixed definite article:

• kaffið = the coffee

So the sentence does not mean she wants a specific known coffee. It means she wants some amount of coffee.

Because Icelandic main clauses usually follow the verb-second pattern.

That means the finite verb typically comes in the second position of the clause:

• Hún = first element
• vill = second element

After that, words like bara and the object phrase can follow.

So this sentence has a very standard order:

• Hún
• vill
• bara
• smá kaffi

For a beginner, this is a good model sentence to copy.

Usually it means a small amount of coffee, not necessarily a physically small cup.

That is an important difference:

• smá kaffi focuses on quantity
• it does not directly describe the size of the container

So the idea is closer to:

• just a little coffee
• some coffee
• only a bit of coffee

The exact interpretation depends on context, but quantity is the main idea.

Yes. Hún vill fá smá kaffi is also a very natural sentence.

Adding fá gives the sense of:

• she wants to get some coffee
• she would like to have some coffee

Without fá, Hún vill bara smá kaffi is still completely normal. It is shorter and more direct:

• she just wants a little coffee

So both are good, but the sentence you were given is perfectly idiomatic Icelandic.