She's often late for school on rainy days.

Literal

She [topic-は] rain [genitive-の] day [on-には] often school [for-に] is-late.

雨の日 ('rainy day') is a transparent compound: 雨 ('rain') + の (genitive) + 日 ('day'). The には after 日 stacks the location particle に with topic は, giving a topicalized time-frame: 'as for on rainy days...' This emphasis is subtle but real — it sets up rainy days as the contrastive class of days under discussion. よく ('often') sets the frequency, and ~に遅れる ('be late for') takes its target with に — 'late for X' rather than 'late from X.'