Learn Dutch: Zwemmen is daar verboden. - Swimming is forbidden there.

You can say Je mag daar niet zwemmen (You are not allowed to swim there). Using the word verboden (forbidden) is just another very common way to express that something is not permitted.

Why does the verb zwemmen act as the subject here?

In Dutch, you can use the full infinitive (the dictionary form) of a verb to act as a noun. It works exactly like the English '-ing' form. So in this sentence, zwemmen literally translates to 'swimming'.

Can I move daar to the start of the sentence?

Yes, you can say Daar is zwemmen verboden. But remember the strict Dutch 'verb second' rule: because daar takes the first position, the verb is must stay in the second position, pushing the subject zwemmen to the third position.

Is verboden a verb or an adjective here?

In this sentence, verboden acts as an adjective describing the swimming as 'forbidden'. It comes from the verb verbieden (to forbid). You will see verboden on warning signs all over the Netherlands and Flanders!