All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The 'Eed in Islam are determined by the Islamic Sharee'ah through the words of our Prophet .
It was narrated on the authority of Anas that:
When the Prophet arrived in Medina, the people had two days in which they celebrated and amused themselves, so he asked them: "What are these two days?" They said, "They are two days in which we used to amuse ourselves in Jahiliyyah (the pre-Islamic period of ignorance)." So the Prophet said: "Indeed, Allaah Almighty has given you, in place of them, what is better than them: The Day of Al-Adhha and The Day of Al-Fitr." [Abu Daawood]
Moreover, it has also been narrated on the authority of Anas that he said: "The Messenger of Allaah came to Medina, and its people had two days in which they would have fun and celebrate, so he said to them: 'Verily Allaah has given you two days that are better than them: The Day of Al-Adhha and the Day of Al-Fitr.'” [Abu Daawood and At-Tirmithi]
This Hadeeth provides evidence that the 'Eed of the Muslims are two days: the Day of Al-Fitr and the Day of Al-Adh-ha, to which the days of Tashreeq are joined, based on the Hadeeth which reads: "The Day of Al-Fitr, the Day of Al-Adhha and the Days of At-Tashreeq are our 'Eed, we the people of Islam." [At-Tirmithi: authentic]
Ash-Shawkani said: "This Hadeeth implies evidence that the days of At-Tashreeq, which follow the Day of An-Nahr (the day of Al-Adhha), are considered days of 'Eed."
The days of At-Tashreeq are the three days following the day of An-Nahr, as stated in Al-Muntaqa Sharh Al-Muwatta’: "As for the days of At-Tashreeq, they are the three days that come after the day of An-Nahr."
Many Ahadeeth highlight that showing happiness and joy is recommended during the days of 'Eed. There are several meanings and points of significance of 'Eed in Islam, some of which are: It is related to religious seasons; for 'Eed Al-Fitr is related to the end of fasting the month of Ramadan, and 'Eed Al-Adhha is related to the season of Hajj and follows the day of ‘Arafah.
The 'Eed of Al-Fitr is related to the end of fasting Ramadan; the month when the Quran was revealed. The Quran is the divine methodology whereby Allaah Almighty outlined the features of the straight path for establishing this Ummah (community). Hence, it is suitable that the day that follows the end of this month be a day of 'Eed, as a way to express gratefulness to Allaah, the Exalted, for the blessing of revealing the Noble Quran that He bestowed upon us in this month, and of granting us success to abide by His commands and avoid His forbiddances. Also, it is a way to purify our souls and remind them of the blessings that Allaah Almighty bestowed upon them.
The same applies to 'Eed Al-Adh-ha, as it reminds us of the day when the favor was completed and perfected. It comes after the day when Allaah Almighty revealed to His Messenger : the proclamation of completing the religion, perfecting the favor, and His satisfaction with Islam as a religion for us. This occurred when Allaah Almighty revealed to his honorable Messenger on the day of ‘Arafah in the tenth year A.H., as he led the procession of the great Hajj, the verse (which means): {This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion.} [Quran 5:3]
It is fitting for us to annually celebrate the days that mark the beginning and the completion of the religion by making them days of 'Eed: the first is 'Eed Al-Fitr and the second is 'Eed Al-Adh-ha.
Allaah Knows best.