Praise be to Allah.
The greatest day of Hajj is the Day of Sacrifice, which is the tenth day of Dhu’l-Hijjah. Abu Dawood narrated from Ibn ‘Umar (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) stood up on the day of Sacrifice during the Hajj that he performed and said: “What day is this?” They said, “the Day of Sacrifice.” He said, “This is the greatest day of Hajj.” Sunan Abi Dawood, 1945; classed as saheeh by al-Albaani in Saheeh Abi Dawood, 1700.
Al-Bukhaari (369) narrated that Abu Hurayrah (may Allaah be pleased with him) said: Abu Bakr al-Siddeeq (may Allaah be pleased with him) sent me amongst the announcers to proclaim in Mina on the Day of Sacrifice, “After this year no mushrik is allowed to perform Hajj or to circumambulate the House naked.”
The Day of Sacrifice is called the greatest day of Hajj because during that night there is the standing at ‘Arafah and staying overnight in al-Mash’ar al-Haraam, and during that day there is the stoning of the Jamrah, offering the sacrifice, shaving the head, tawaaf and saa’i, which are all actions of Hajj. The day of Hajj refers to the time and the description of greatest refers to the actions done at that time. The greatest day of Hajj is mentioned in the Qur’aan where Allaah says (interpretation of the meaning):
“And a declaration from Allaah and His Messenger to mankind on the greatest day (the 10th of Dhul-Hijjah — the 12th month of Islamic calendar)”
And Allaah is the Source of strength.