When Allah's Messenger (sallallaahu 'alaihi wasallam) came to Medina, he found the jews fasting on the day of 'Ashura' (i.e. 10th of Muharram). They used to say: "This is a great day on which Allah saved Moses and drowned the folk of Pharaoh. Moses observed the fast on this day, as a sign of gratitude to Allah."
The Prophet said, "I am closer to Moses than they." So, he observed the fast (on that day) and ordered the Muslims to fast on it.

- Sahih Bukhari