Nasai

(1) Among these days, the Day of Arafah is an Eid only for the pilgrims, because on this day they gather together and perform the rituals of Hajj. The rest of the Muslims do not do anything special on this day; therefore, it is not an Eid for them. They can fast on this day; in fact, it is recommended (mustahabb) and superior. However, the pilgrims cannot fast on this day at Arafah because it is their Eid, and moreover, on this day they have to perform difficult tasks themselves. Going from Mina to Arafat and enduring the severity of the weather and the hardship of the gathering is a matter of courage and endurance. There is a strong likelihood that fasting on this day would cause them hardship; therefore, fasting is prohibited for them. Other people are in their homes; they can fast on this day. For them, this will be a deed of special reward. The following days, that is, the Day of Sacrifice (Yawm al-Nahr) and the Days of Tashreeq, are Eid for all Muslims because everyone slaughters sacrifices and enjoys the hospitality of Allah during these days. These four days and the day of Eid al-Fitr are days of eating and drinking for all the people of Islam; therefore, fasting on all these days is prohibited for all Muslims everywhere.

(2) The reason for the naming of the Days of Tashreeq is that during these days people would cut the meat of the sacrifice into thin slices and dry it in the sun so that it would not spoil and could be used later. Cutting the meat into thin slices and drying it in the sun is called "tashreeq" in the Arabic language.

English Commentary:
1:
By "Yawm Arafah" is meant the day on which the pilgrims are present in the plain of Arafat, that is, the 9th of Dhu al-Hijjah according to the sighting in Makkah al-Mukarramah.

2:
The day of sacrifice, that is, the 10th of Dhu al-Hijjah.

3:
By "Ayyam al-Tashreeq" are meant the 11th, 12th, and 13th of Dhu al-Hijjah.

Benefits and Issues:
The days of Tashreeq are, in essence, the days of Eid themselves.
During these days, it is not permissible to observe general voluntary fasting.
However, if a person performing Hajj Tamattu‘ does not have the means to offer a sacrificial animal, then ten fasts become obligatory upon him:
Three days during the days of Hajj, and seven after returning home.
Thus, he is permitted to observe these fasts during the days of Tashreeq.
It is mentioned in Surah Al-Baqarah: (So whoever performs ‘Umrah [during the Hajj months] followed by Hajj [offers] whatever offering is easy [for him]. But whoever cannot find [or afford it]—then a fast of three days during Hajj and of seven when you have returned [home]; these are ten complete [days].) ( Al-Baqarah: 196)
However, regarding the mention of the Day of ‘Arafah in this context—that fasting on this day is also not valid—this ruling is for the pilgrims.
For them, it is better not to fast, so that they may perform the worship of standing in ‘Arafat properly.
But for non-pilgrims, the virtue of fasting on the Day of ‘Arafah (9th Dhul-Hijjah) is that it is an expiation for the sins of two years for them.