Why is nous repeated in the phrase nous nous lavons?

The first nous is as you understand it -- the subject pronoun 'we'. The second nous is the direct object meaning ourselves.

The infinitive of the verb is se laver, a reflexive verb. Unlike regular verbs, such as vendre, these verbs always have a reflexive pronoun. The other pronouns of this type are me, te, se, vous, and se (again for ils/elles). For instance, je me lave.