Learn Farsi: مرداد ماهِ گرمی است.

That ی is the indefinite suffix, meaning 'a' or 'an'. Instead of putting یک (one/a) at the beginning, Farsi often adds ی at the end to make a phrase indefinite. So ماهِ گرمی means 'a hot month'.

If the ی means 'a', why does it attach to the adjective (گرم) instead of the noun (ماه)?

In Farsi, when a noun is followed by an adjective connected by the ezafe (the short 'e' sound linking words), the indefinite ی attaches to the very end of that entire group. The core phrase is ماهِ گرم (hot month). Adding the ی to the end gives you ماهِ گرمی (a hot month).

What exactly is مرداد?

مرداد (Mordad) is the fifth month of the Iranian solar calendar. It corresponds roughly to late July and most of August, which is the peak of summer. That is why the sentence specifically notes it is a hot month!

How would you say this sentence in everyday spoken Farsi?

In casual speech, the formal verb است (is) usually shrinks and attaches to the previous word. Because گرمی ends in a vowel sound, an extra 'y' sound bridges the gap, making it گرمیه (garmi-ye). So in everyday conversation, you will hear: مرداد ماهِ گرمیه.