In general use, refers to rain that is falling strongly. In Japan Meteorological Agency terminology, specifically denotes rainfall of 20–29 mm per hour.
See also: 気象庁
It's raining so heavily that I get wet even with an umbrella.
According to the JMA, we need to be careful of heavy rain tonight.
Compound of 強い (strong, intense) and 雨 (rain). The JMA-specific definition is a technical usage of the same phrase.