There are only two annual festivals in Islam. They are: (1) The Festival of Fast Breaking (‛Eed-ul-Fitr), which is celebrated on the first day of the lunar month of Shawwaal, and (2) the Festival of Sacrifice (‛Eed-ul-Adha), which is celebrated on the tenth day of the lunar month of Dhul-Hijjah.
Festivals represent apparent rituals of religion. When the Prophetﷺ arrived in Madinah, he found that the people there had set aside two days in the year for fun. He asked them, ‘‘What are these two days?” “We used to play and have fun on these days before the advent of Islam,” they replied. The Prophetﷺ then said, “Allah has given you two better days: ‛Eed-ul-Fitr and (‛Eed-ul-Adhaa.” Sunan Abu Dawud: 1134, classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 2021. Explaining that festivals represent the religion of their followers, he once observed, “Every nation has a festival, and this is our festival.” Sahih Al-Bukhari: 909; Sahih Muslim: 892
‛Eed-ul-Fitr falls on the first day of the lunar month of Shawwaal, marking the end of the month-long Ramadaan fast. Just as fasting during the month of Ramadaan is an act of worship, celebrating ‛Eed-ul-Fitr is also an act of worship whereby Muslims express their gratitude to Allah for enabling them to perform this act of worship and for completing His grace upon them. As the Qur’an states, “You should complete the number of days and proclaim Allah’s greatness for the guidance He has given you so that you will be thankful.” Quran Soorat Al-Baqarah, 2:185 
Eid al-Adha is the tenth day of Dhu’l-Hijjah, the last (twelfth) month of the Hijri or Islamic calendar. It is, as the Prophet (peace be upon him) said: “The greatest day in the sight of Allaah, may He be blessed and exalted, the Day of Sacrifice . . .” Abu Dawud 1765; Saheeh al-Jaami‘, 1064 It is also the greatest day of Hajj, as the Prophet (peace be upon him) told us. al-Tirmidhi, see Saheeh al-Jaami‘, 8191
The reason why it is described as the greatest day of the year is that it combines so many acts of worship which are not combined on any other day, such as the Eid prayer, offering the sacrifice, reciting Takbeer (glorifying Allaah), and widespread remembrance of Allaah. For the pilgrims in Makkah, it also includes offering a sacrifice, stoning the pillars representing Shaytaan (the devil), shaving the head (for men only; women merely cut a little off their hair), and performing Tawaaf (circumambulation of the Ka‘bah) and Sa‘ee (running between the two hills of Safaa and Marwa). 
Allaahu akbar, Allaahu akbar, laa ilaaha ill allaah, Allaahu akbar, Allaahu akbar, walillaahil-hamd (Allah is the Greatest, Allah is the Greatest; there is no god worthy of worship except Allah; Allah is the Greatest, Allah is the Greatest; all praise belongs to Allah).
One may also recite the following: Allaahuakbaru kabeeran, wal-hamdu lillaahi katheeran, wa subhaan-Allaahi bukratan waaseelaa (Allah is the Greatest;His is the abundant praise, and glory be to Him day and night).
Men generally pronounce the Takbeer aloud, but without disturbing other people; women, however, pronounce it quietly.