She became a nurse.

Literal

She [topic-は] nurse [become-に] became.

なる ('to become') takes に for what one becomes — the same に of result-of-change that recurs across Japanese (有名になる 'become famous,' 大人になる 'become an adult'). The pattern is so productive it's the default way of expressing change of state in Japanese, including for occupations: 看護婦になる, 先生になる, 医者になる. English's 'become a doctor' loses the structural detail Japanese keeps — that the new role is the *destination* of change, not just an attribute one gains.