To rain very hard

There's a storm warning and the forecast says that later today rain will come down to beat the band with zero visibility

È stato diramato un avviso di tempesta e le previsioni dicono che in giornata pioverà come Dio la manda con visibilità zero

We had to stop on the highway shoulder for a while because it was raining to beat the band and even the windscreen wiper was useless

Ci siamo dovuti fermare sulla banchina dell'autostrada per un po' perché pioveva come Dio la mandava e il tergicristallo non puliva più niente

"To beat the band" is an American expression which dates only to early 1900s, a time when parades and band concerts were very popular. Its origin seems to have been literal: the desire to arrive at some spots before a band or musicians leading a parade had passed that spot, so that one could watch the entire parade. Therefore, one had to get there as quickly as possible, either by running or by whipping up his horse.
According to another theory, it means "make more noise than a loud band".