In June it rains day after day.

Literal

June [topic-は] coming day [also-も] coming day [also-も] rain [subject-が] falls.

来る日も来る日も ('day after day, every single day') is an emphatic repetition pattern. It captures the relentless nature of Japan's 梅雨 (rainy season), which typically starts in June. The repetition itself mimics the monotony of endless rain.