Hon vill baka en kaka till fikat.

Vill is the present tense of the irregular verb vilja, which means to want.

• vilja = to want
• vill = want / wants

So Hon vill means she wants.

Other forms:

• ville = wanted
• velat = wanted (supine/past participle use in compound tenses)

Because vill is a modal verb-like verb in Swedish, and after verbs like this, Swedish usually uses the bare infinitive.

So you say:

• Hon vill baka = she wants to bake

not:

• Hon vill att baka

This is similar to other Swedish verbs such as:

• kan baka = can bake
• ska baka = will/is going to bake
• måste baka = must bake

Baka is the infinitive form, meaning to bake.

After vill, Swedish uses the infinitive directly:

• vill baka = wants to bake

Compare:

• baka = to bake
• bakar = bakes / is baking
• bakade = baked
• bakat = baked

Because kaka is an en-word in Swedish, not an ett-word.

Swedish nouns have two grammatical genders in modern standard Swedish:

• en words
• ett words

Since kaka is an en-word, the indefinite singular is:

• en kaka

not:

• ett kaka

• en kaka = a cake / a cookie (indefinite singular)
• kakan = the cake / the cookie (definite singular)

So in your sentence, en kaka means she wants to bake a cake, not a specific one already known.

If it were a specific cake, you would say:

• Hon vill baka kakan till fikat.

Yes, sometimes it can, depending on context.

In Swedish, kaka can be a general word for a baked sweet item, and in some contexts it may be closer to cookie, biscuit, or cake. Context tells you what is meant.

A few related words:

• kaka = cake/cookie in a broad sense
• småkaka = small cookie
• tårta = layer cake / celebration cake

In baka en kaka, many learners will naturally understand it as bake a cake, but the exact type depends on context.

Here till means something like for.

So till fikat means:

• for fika
• for the coffee break
• for the snack/coffee time

It tells you the purpose of the cake: she wants to bake it for that occasion.

Because fikat is the definite form of the noun fika.

• fika = a fika / coffee break / coffee-and-snack time
• fikat = the fika

So till fikat literally means for the fika.

In Swedish, the definite form is often used when talking about a specific planned or understood occasion, even when English might sound more natural with just for fika or for the coffee break.

It can be both.

As a noun:

• en fika = a coffee break / coffee-and-snack break

As a verb:

• att fika = to have fika / to take a coffee break

Examples:

• Vi tar en fika. = We’re having a fika.
• Vi fikar. = We’re having coffee / taking a fika break.

In your sentence, fikat is a noun, not a verb.

The sentence follows normal Swedish main-clause word order:

• Hon = subject
• vill = finite verb
• baka = infinitive
• en kaka = object
• till fikat = adverbial/prepositional phrase

So:

Hon | vill | baka | en kaka | till fikat

A useful rule is that in Swedish main clauses, the finite verb usually comes in second position. This is often called the V2 rule.

You add inte after the finite verb in a main clause:

• Hon vill inte baka en kaka till fikat.

That means She does not want to bake a cake for fika.

Position:

• Hon = subject
• vill = finite verb
• inte = negation
• baka = infinitive

So the pattern is:

subject + finite verb + inte + infinitive ...