Da jeg kom hjem, stod der en skål med yoghurt og banan på bordet, som min søster havde lavet til mig.

Here Da means when, referring to one specific moment in the past: when I got home.

Danish usually uses:

• da for a single past event
• når for something habitual, general, or in the future

So:

• Da jeg kom hjem = When I got home
• Når jeg kommer hjem = When I get home / Whenever I come home

Because this sentence describes one completed past situation, da is the natural choice.

This is because Danish main clauses follow the verb-second rule.

The opening part Da jeg kom hjem takes up the first position in the sentence. After that, the finite verb of the main clause must come next:

• Da jeg kom hjem, stod der en skål ...

So stod comes immediately after the introductory clause.

If you started a sentence without that opening clause, you could say:

• Der stod en skål på bordet.

But once Da jeg kom hjem is placed first, the order changes:

• Da jeg kom hjem, stod der en skål på bordet.

This der is an expletive or dummy word, like English there in there was or there stood.

So:

• Der stod en skål på bordet
  = There was / there stood a bowl on the table

It does not mean physical there in the sense of a location here. It is just used to introduce the existence of something.

This is a very common Danish pattern:

• Der er en bog på stolen. = There is a book on the chair.
• Der lå en kat i haven. = There was a cat lying in the garden.

Danish very often uses position verbs where English would often just say was.

Common ones are:

• stå = stand
• ligge = lie
• sidde = sit

A bowl on a table is thought of as standing upright, so Danish naturally says:

• Der stod en skål på bordet.

English can say There was a bowl on the table, but Danish often prefers the more specific verb.

Using var would not be impossible in every context, but stod sounds more natural and vivid here.

Because hjem and hjemme are different:

• hjem = homeward / to home, showing movement
• hjemme = at home, showing location

So:

• jeg kom hjem = I came home
• jeg er hjemme = I am at home

Since the sentence is about movement toward home, hjem is correct.

This is about Danish noun gender and definiteness.

• skål is a common-gender noun, so its indefinite article is en
  • en skål = a bowl
• bord is a neuter noun
  • et bord = a table

When Danish makes a noun definite, it usually adds the article as a suffix:

• bordet = the table

So:

• en skål = a bowl
• på bordet = on the table

In other words, English uses a separate word the, while Danish often adds -en or -et to the noun.

After med, Danish often lists ingredients as bare nouns, especially in everyday speech.

So:

• en skål med yoghurt og banan
  means a bowl with yogurt and banana

This sounds like describing the contents or ingredients, not counting separate items one by one.

Why singular banan?

Because Danish can use a singular noun in this kind of ingredient-style description. It suggests banana as an ingredient, not necessarily one whole banana as a countable object in focus.

You could also hear other versions depending on context, such as:

• med bananer if several bananas are meant
• med yoghurt og en banan if the speaker wants to emphasize one whole banana

But the original wording is natural.

På bordet means on the table.

The definite form bordet is used because the table is treated as known from the situation. In context, it is probably the table in the home, so Danish does not need to introduce it as new information.

Compare:

• på et bord = on a table
• på bordet = on the table

The sentence uses the definite form because the speaker is talking about a specific, understood table.

Here som means that or which as a relative pronoun:

• som min søster havde lavet til mig
  = that my sister had made for me

The intended meaning is that the sister made the bowl of yoghurt and banana for the speaker.

However, the placement can create a small ambiguity, because the relative clause comes right after bordet, so a learner might briefly wonder whether it refers to the table. Context makes the intended meaning clear, but structurally it is a little loose.

A clearer version might be:

• Da jeg kom hjem, stod der en skål med yoghurt og banan, som min søster havde lavet til mig, på bordet.
• or more simply: Da jeg kom hjem, stod der en skål med yoghurt og banan på bordet. Min søster havde lavet den til mig.

So yes: som means that/which, and the intended referent is the food/bowl, even if the sentence could momentarily feel ambiguous.

Havde lavet is the past perfect.

It shows that one past action happened before another past action:

• jeg kom hjem = I got home
• min søster havde lavet = my sister had made it before that

So the timeline is:

1. the sister prepared it
2. then the speaker came home

That is exactly what the past perfect is for.

Compare:

• lavede = simple past, less clear about the earlier-before-later relationship
• har lavet = present perfect, linked to the present, so it does not fit as well here

Yes. In everyday Danish, lave is extremely common and broad. It often means make, do, or prepare, and it is very often used about food.

So:

• min søster havde lavet til mig
  means my sister had made/prepared it for me

This is very natural Danish.

There are more specific verbs, such as tilberede, but those are often more formal or more specific. In ordinary conversation, lave is usually the normal choice.

Here til mig means for me in the sense of intended for me or made for me to have.

With food, gifts, and things prepared for a person, til is very common:

• Hun lavede morgenmad til mig. = She made breakfast for me.

For mig can also mean for me in English, but it often has slightly different uses, such as:

• on my behalf
• instead of me
• from my point of view

So in this sentence, til mig is the most natural choice because it focuses on the speaker as the recipient of what the sister prepared.