She doesn't need to go to school on Saturday.

Literal

Saturday [on-に] school [to-に] go need [topic-は] not-exist.

~必要はありません is the polite negative of ~必要がある ('there is a need to'). It's more formal than ~なくてもいい — you'd hear it in official announcements or careful speech. The は after 必要 adds a contrastive nuance: 'the need (specifically) does not exist,' implying other obligations might still apply.