。
It's really started to rain in earnest.
Literal
Full-scale-ly rain [subject-が] fall-begin-[past-た].
本格的に ('in earnest, in full force') is the adverbial form of the な-adjective 本格的 ('full-scale, authentic, serious'). 降り出す ('to start raining/falling') is a compound verb: 降る ('fall') + 出す ('start'). The ~出す compound auxiliary is productive, meaning 'begin doing X suddenly or abruptly' — contrasts with ~始める which is a more neutral 'begin.'