General
What is the wisdom behind the actions of Hajj and Umrah?
The texts point to the general wisdom of Hajj and Umrah: affirming the oneness of Allah, remembering Him, and benefits for the pilgrims in this world and the Hereafter (see Surah al-Hajj 22:27-30).
Tawhid: the pilgrim begins with the Talbiyah, “Labbayka Allahumma labbayk, labbayka la sharika laka labbayk”, declaring that Allah has no partner, and every rite after it is done for Allah alone.
Remembrance: the Prophet (peace and blessings of Allah be upon him) said that Tawaf, Sa'i and the stoning of the Jamarat were only ordained to establish the remembrance of Allah.
Benefits: Muslims from every land gather in the same clothing, at the same time and in the same place, doing the same acts. They come to know one another, and the poor are fed from the sacrifice.
There is also clear wisdom in the order of the rites. Ihram and the Talbiyah announce that the rites have begun. Tawaf comes first on reaching Makkah because the Kaaba is the greatest thing in the Haram, and Sa'i follows because Safa and Marwa are the nearest thing to it. In Hajj, Mina is preparation for standing at Arafah, the greatest pillar; Muzdalifah is on the way back and gives rest before the Day of Sacrifice; the stoning, the sacrifice and shaving the head fall on the day of Eid; then comes Tawaf in gratitude for completing the greatest rites, then the days of Mina for remembrance and sacrifice, and the farewell Tawaf at departure.
Scholars have also mentioned wisdom behind particular acts:
The Ihram garments: a reminder of the Day of Resurrection, a lesson in humility, and equality between rich and poor.
Kissing the Black Stone: an act of worship done in obedience, following the Prophet (peace and blessings of Allah be upon him). ‘Umar (may Allah be pleased with him) said that he knew it was a stone that could neither harm nor benefit, and that he kissed it only because he saw the Prophet kiss it. It is not kissed to seek blessing from it.
Sa'i: it goes back to Hajar, who went seven times between Safa and Marwa seeking help for her son Isma'il. The pilgrim remembers that his need for Allah is like hers, and that Allah does not forsake those who obey Him.
Stoning the Jamarat: following Ibrahim (peace be upon him), who stoned the Shaytan there, and a sign of enmity towards the Shaytan.
Most of these details are the scholars' own reasoning and are not stated in a text. Some scholars said that the rites were prescribed in this way as a test of obedience, so a Muslim follows them whether the wisdom is known or not. The pilgrim should keep his time for the remembrance of Allah and honour His symbols as they deserve.