Muslims celebrate only two Eids (festivals): Eid al-Fitr (at the end of the month of Ramadan), and Eid al-Adha, which marks the completion of the Hajj (annual pilgrimage period) on the 10th day of the month of Dhul-Hijjah.

During these two festivals, Muslims congratulate one another, spread joy in their communities, and celebrate with their extended families. But more importantly, they remember Allah's blessings on them, celebrate His name and offer the Eid prayer in the mosque. Other than these two occasions, Muslims do not recognize or celebrate any other days in the year.

Of course, there are other joyous occasions for which Islam dictates appropriate celebration, such as wedding celebrations (walima) or on the occasion of the birth of a child (aqeeqah). However, these days are not specified as particular days in the year; rather, they are celebrated as they happen in the course of a Muslim's life.

On the morning of both Eid al-Fitr and Eid al-Adha, Muslims attend Eid prayers in congregation at the mosque, followed by a sermon (khutbah) that reminds Muslims of their duties and responsibilities. After the prayer, Muslims greet each other with the phrase "Eid Mubarak" (Blessed Eid) and exchange gifts and sweets.

Eid al-Fitr

Eid al-Fitr marks the end of Ramadan, which takes place during the ninth month of the lunar-based Islamic calendar.

Eid al-Fitr is important because it follows one of the most sacred months of all: Ramadan. Ramadan is a time for Muslims to strengthen their bond with Allah, recite the Qur’an and increase in good deeds. At the end of Ramadan, Allah gives Muslims the day of Eid al-Fitr as a reward for successfully completing the fast and for increasing in acts of worship during the month of Ramadan. On Eid al-Fitr, Muslims thank Allah for the opportunity to witness another Ramadan, to come closer to Him, to become better people and to have another chance to be saved from Hellfire.

It was narrated from Talhah bin ‘Ubaidullah that two men came to the Messenger of Allah ﷺ (peace be upon him). They had become Muslim together, but one of them used to strive harder than the other. The one who used to strive harder went out to fight and was martyred. The other one stayed for a year longer, then he passed away. Talhah said: “I saw in a dream that I was at the gate of Paradise and I saw them (those two men). Someone came out of Paradise and admitted the one who had died last, then he came out and admitted the one who had been martyred. Then he came back to me and said: ‘Go back, for your time has not yet come.’” The next morning, Talhah told the people of that and they were amazed. News of that reached the Messenger of Allah ﷺ (peace be upon him) and they told him the story. He said: “Why are you so amazed at that?” They said: “O Messenger of Allah, the first one was the one who strove harder, then he was martyred, but the other one was admitted to Paradise before him. The Messenger of Allah ﷺ (peace be upon him) said: “Did he not stay behind for a year?” They said: “Yes.” He said: “And did not Ramadan come and he fasted, and he offered such and such prayers during that year?” They said: “Yes.” The Messenger of Allah ﷺ (peace be upon him) said: “The difference between them is greater than the difference between heaven and earth.”

Sunan Ibn Majah, 3925

Eid al-Adha

Eid al-Adha marks the completion of the annual Hajj period (pilgrimage to Mecca), which takes place in the month of Dhul-Hijjah, the twelfth and final month of the lunar-based Islamic calendar.

The celebration of Eid al-Adha is to commemorate prophet Ibrahim’s (Abraham) devotion to Allah and his readiness to sacrifice his son, Ismail (Ishmael). At the very point of sacrifice, Allah replaced Ismail with a ram, which was to be slaughtered in place of his son. This command from Allah was a test of prophet Ibrahim’s willingness and commitment to obey his Lord’s command, without question. Therefore, Eid al-Adha means the festival of sacrifice.

One of the best deeds for Muslims to perform on Eid al-Adha is the act of Qurbani/Uhdiya (sacrifice), which is carried out following the Eid Prayer. Muslims sacrifice an animal in order to remember Prophet Abraham's sacrifice for Allah. The sacrificial animal must be a sheep, lamb, goat, cow, bull or a camel. The animal must be in good health and over a certain age in order to be slaughtered, in a halal, Islamic way. The meat of the sacrificed animal is shared among the person making the sacrifice, their friends and family and the poor and needy.

Sacrificing an animal on Eid al-Adha reflects prophet Abraham's readiness to sacrifice his own son and it is also an act of worship found in the Quran and a confirmed tradition of prophet Muhammad ﷺ (peace be upon him).

The Prophet ﷺ (peace be upon him) slaughtered two rams, black and white in color (as sacrifices), and I saw him putting his foot on their sides and mentioning Allah's Name and Takbir (Allahu Akbar). Then he slaughtered them with his own hands.

Sahih al-Bukhari, 5558

In the Quran, God has said:

And complete the Hajj and ʿUmrah for Allah. But if you are prevented, then [offer] what can be obtained with ease of sacrificial animals. (...)

Quran - 2:196

(interpretation of the meaning)

Source: islamqa.info