When unexpected heavy rain starts falling on a warm evening. The rain allows you to feel excited about the fact that you're so into each other you don't mind getting wet and the temperature prevents you from becoming shivery and unattractive.
Date rain can happen during the day but it's significantly less romantic.
Note: you do not have to be on a date for the term to apply.
"The weather was supposed to be bad but it turned out to just be date rain."