Learn Dutch: Terwijl ik fiets, bel ik mijn broer. - While I cycle, I call my brother.

Because the sentence starts with a subordinate clause (Terwijl ik fiets). Whenever a sentence starts with a subordinate clause, the main clause that follows it must use inversion, meaning the verb comes before the subject. Therefore, it is bel ik instead of ik bel.

Why does the verb fiets come right after ik in the first part? Don't verbs go to the end in a subordinate clause?

They do! Terwijl introduces a subordinate clause, which pushes all verbs to the end. Because there is only one verb in this clause (fiets), the end of the clause happens to be right after the subject.

Is the comma important here?

Yes, the comma is very helpful. In Dutch, a comma usually separates the subordinate clause from the main clause. Right after that comma is exactly where you must apply the inversion and put your main verb (bel) first.

How would the word order change if I started with the main clause instead?

If you start with the main clause, you use normal word order: Ik bel mijn broer. The subordinate clause still pushes its verb to the end: terwijl ik fiets. The whole sentence becomes Ik bel mijn broer terwijl ik fiets. There is no inversion here because the sentence starts with the main subject.