godan verb (-ku), intransitive verb
continue to rain or snow
Used for rain or snow that keeps falling without stopping. Often appears in weather reports and everyday descriptions.
昨日から雨が降り続いている。
It has been raining continuously since yesterday.
雪が一晩中降り続いた。
It snowed all night long.
降る is the basic verb for 'to fall' (rain/snow), while 降り続く emphasizes the continuous, ongoing nature of the precipitation.
Compound of 降り (continuative form of 降る 'to fall') + 続く 'to continue'.