Fasting on the Day of عرفة (the 9th of ذو الحجة) is one of the most virtuous voluntary fasts in Islam for those who are not performing الحج. النبي (صلى الله عليه وسلم) was asked about fasting on the Day of عرفة and said: 'It expiates the sins of the previous year and the coming year.' This tremendous reward makes it one of the most highly مستحب acts of worship for non-الحجاج.
However, الحجاج who are actually at عرفة performing الحج are advised NOT to fast on this day. النبي (صلى الله عليه وسلم) himself did not fast on the Day of عرفة during his الحج. The reason is practical and spiritual — the Day of عرفة requires immense physical and spiritual energy. Pilgrims are standing in extreme الحرارة for hours, making intense الأدعية, 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 النبي at عرفة, and he drank it publicly to show people he was not fasting.
For non-الحجاج around the world, this fast is separate from the Days of التشريق (11th-13th ذو الحجة), on which fasting is prohibited. The Day of عرفة fast is standalone and carries its immense reward independently. Combined with increased dhikr, دعاء, and charity on this day, non-الحجاج can spiritually participate in the blessings of the الحج season from wherever they are.