Fasting on the Day of Arafat (the 9th of Dhul Hijjah) is one of the most virtuous voluntary fasts in Islam for those who are not performing Hajj. The Prophet (peace be upon him) was asked about fasting on the Day of Arafat and said: 'It expiates the sins of the previous year and the coming year.' This tremendous reward makes it one of the most highly recommended acts of worship for non-pilgrims.
However, pilgrims who are actually at Arafat performing Hajj are advised NOT to fast on this day. The Prophet (peace be upon him) himself did not fast on the Day of Arafat during his Hajj. The reason is practical and spiritual — the Day of Arafat requires immense physical and spiritual energy. Pilgrims are standing in extreme heat for hours, making intense supplications, and need their strength. Fasting could compromise their ability to worship fully. There was even a narration where Umm al-Fadl sent a container of milk to the Prophet at Arafat, and he drank it publicly to show people he was not fasting.
For non-pilgrims around the world, this fast is separate from the Days of Tashreeq (11th-13th Dhul Hijjah), on which fasting is prohibited. The Day of Arafat fast is standalone and carries its immense reward independently. Combined with increased dhikr, dua, and charity on this day, non-pilgrims can spiritually participate in the blessings of the Hajj season from wherever they are.