The Messenger of Allah (PBUH) said to a man from Aslam (a tribe), announce among your folks or among people on the day of 'Ashura': Whoever had eaten, let him fast for the rest of his day, and whoever had not eaten, let him fast.
The people of pre-Islamic times of ignorance used to fast on the day of 'Ashura', and that the Messenger of Allah (PBUH) and Muslims had fasted it before fasting of Ramadan was prescribed. When it was prescribed, the Messenger of Allah (PBUH) said: 'Ashura' is one of the days of Allah Almighty. So whoever wishes may fast it, and whoever wishes may leave it.
The Messenger of Allah (PBUH) came to Medina and found that the Jews had fasted on the day of 'Ashura'. He asked them about that, and they said: This is the day on which Moses prevailed over Pharaoh. The Prophet (PBUH) said to his companions: You have more claim to Moses than they do, so fast on it.
A man asked the Prophet (PBUH) about fasting on the Day of 'Arafah? The Prophet (PBUH) replied: I have the best expectation of Allah that he will expiate the previous year and the coming one. The man said: O Messenger of Allah, what about fasting on 'Ashura'? The Prophet (PBUH) replied: I have the best expectation of Allah that he will expiate the previous year.