Toen de ketting eraf viel, moest Anna naar huis lopen.

Here toen means when.

It introduces a specific event in the past:

• Toen de ketting eraf viel... = When the chain came off...

A useful comparison:

• toen = when for a particular past moment
• als = when/if for repeated situations, general truths, or conditions

So toen is the natural choice here because this is one specific past event.

Because toen introduces a subordinate clause.

In Dutch subordinate clauses, the finite verb usually goes to the end. So:

• de ketting viel eraf = main clause
• toen de ketting eraf viel = subordinate clause

That is why viel comes last in that part of the sentence.

eraf means something like off or off it.

In this sentence, de ketting eraf vallen means the chain comes off. In context, this is very natural for a bicycle chain coming off the bike.

So:

• eraf vallen = to fall off / to come off

You do not need to translate er very literally every time. In many everyday expressions, eraf works as a fixed particle meaning off it/off there/off.

It behaves a lot like a separable verb construction, even though learners often experience it more as a fixed combination of a verb plus a particle.

Compare:

• main clause: De ketting viel eraf.
• subordinate clause: ... toen de ketting eraf viel.

So the particle eraf stays with the verb meaning-wise, but its position changes depending on clause type.

For learning purposes, it is very helpful to treat eraf vallen as one expression meaning to come off.

Literally it means the chain, but in this context it almost certainly means the bicycle chain.

Dutch often leaves out extra words when the context makes them obvious. If someone then has to walk home, the most natural interpretation is:

• the bike chain came off
• so Anna could not keep riding
• therefore she had to walk home

Because the sentence starts with a subordinate clause:

• Toen de ketting eraf viel, ...

That whole clause takes the first position in the sentence. In Dutch main clauses, the finite verb comes in the second position, so after that opening clause you get:

• ..., moest Anna naar huis lopen.

This is called inversion:

• first: subordinate clause
• second: finite verb moest
• then: subject Anna

If the sentence started directly with Anna, you would say:

• Anna moest naar huis lopen.

Both are in the simple past.

• viel = past of vallen
• moest = past of moeten

Dutch uses the simple past a lot in storytelling and narration, especially in written language and in retelling events.

So this sentence sounds like normal narrative Dutch.

Because moest is a modal verb.

With modal verbs such as moeten, kunnen, willen, mogen, and zullen, the second verb usually appears as an infinitive at the end of the clause:

• Anna moest naar huis lopen.

So the structure is:

• moest = finite verb
• lopen = infinitive at the end

This is very common in Dutch.

Not necessarily.

moesten often means had to because of circumstances, not because someone explicitly gave an order.

Here the idea is probably:

• the chain came off
• she could not continue riding
• so she had to walk home

So it is more like she had no choice than someone told her to do it.

Because naar huis is the normal Dutch expression for going home.

Important difference:

• thuis = at home (location)
• naar huis = to home / homeward (movement)

So:

• Anna is thuis. = Anna is at home.
• Anna gaat naar huis. = Anna goes home.

That is why naar huis lopen means to walk home.

Because naar huis is a fixed idiomatic expression.

Dutch does not normally say naar het huis when it means home.
het huis would mean the house in a more literal sense, usually a specific building.

So:

• naar huis = home
• naar het huis = to the house

Those are not the same.

Yes, but that would mean something slightly different structurally.

• Toen viel de ketting eraf.
  This is a main clause and toen means more like then / at that moment.

In your sentence:

• Toen de ketting eraf viel, ...

Here toen means when and introduces a subordinate clause.

So both are possible Dutch, but they are different sentence patterns with different word order.

It has two parts:

1. Toen de ketting eraf viel
   = subordinate clause

2. moest Anna naar huis lopen
   = main clause

So the pattern is:

• subordinate clause + comma + main clause

And because the subordinate clause comes first, the main clause shows inversion:

• moest Anna instead of Anna moest

That makes this sentence a very useful example of Dutch word order.