Sayyidah Aishah (may Allah be pleased with her) narrates: The day of Ashura was a day on which Quraysh fasted in the Days of Ignorance (Jahiliyyah), and the Messenger of Allah (peace and blessings be upon him) also used to fast on it before prophethood. When he (peace and blessings be upon him) came to Madinah, he (peace and blessings be upon him) fasted on it and ordered that it be fasted. Then when Ramadan was made obligatory, that became the obligation, and the day of Ashura was left. So "whoever wishes may fast on it, and whoever wishes may leave it."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8409