Fig.: an experience that causes a crucial change, a turning point in someone's life; a life-changing experience. Also, in a joking tone, to have a sudden and unexpected good idea or intuition

Paul's trip to that very poor, war-torn Country was a Road to Damascus. Upon his return, he decided to volunteer at a homeless charity

Il viaggio di Paolo in quel poverissimo Paese martoriato dalla guerra è stato una via di Damasco, tanto che al ritorno ha deciso di fare il volontario in un'associazione per i senzatetto

It seemed like a no-win situation, when our boss had his road-to-Damascus moment: all of a sudden he had a brilliant intuition that allowed us to solve all the problems

Sembrava una situazione senza vie di uscita, quando il nostro capo – folgorato sulla via di Damasco – ha avuto all'improvviso un'intuizione geniale che ci ha permesso di risolvere tutti i problemi

The judge of the swimming semifinal had disqualified our athlete for an alleged foul, but then he had his road-to-Damascus moment: there had been no fault, so he canceled the disqualification and admitted our athlete to the final

Il giudice di gara della semifinale di nuoto aveva squalificato l'atleta per un presunto fallo, ma poi si è ravveduto sulla via di Damasco: non c'era stato nessun fallo, per cui ha annullato la squalifica ed ha ammesso il nostro atleta alla finale

The source of this saying, which has been used metaphorically for a long time, is in the Acts of the Apostles (9, 1-9). The story goes that Saul was on his way from Jerusalem to Damascus to persecute Christians, when he was struck by a strong light, that blinded him. Then he heard a divine voice:
"Saul, Saul, why are you persecuting me?" And he said, "Who are you, Lord?" And he said, "I am Jesus, whom you are persecuting. But rise and enter the city, and you will be told what you are to do."
Saul was extremely shaken by the experience, but when after three days, a Christian named Ananias went to him and baptized him, his blindness went away.
Saul, having converted to Christianity, changed his name, becoming Paul, and completely changed his life: from persecutor of Christians, he became "the apostle of the Gentiles"