Learn Swedish: Vi låter kompisarna väsnas i trädgården. - We let the friends make noise in the garden.

Because it follows the causative verb låter (let/allow). Just like in English, Swedish uses låta plus an object (kompisarna) followed by the bare infinitive of the action they are allowed to do (väsnas). Notice that we don't use att (to) before the second verb.

Why does väsnas end in an "s"? Is it a passive verb?

No, it is a deponent verb. These are verbs that always end in -s in all tenses but have an active meaning. The infinitive att väsnas simply means "to make noise". You have likely seen this before with verbs like hoppas (to hope) or andas (to breathe).

I learned that låter means "sounds". How do we know it means "lets" in this sentence?

The verb låta has two common meanings: "to sound" and "to let/allow". You can tell it means "let" here because of the sentence structure. When låta is followed by an object and a second bare infinitive verb, it means someone is letting someone else do something.