Follow up question: How did Muhammad Ahmad convince his followers that he was the 'Mahdi' of Islam?

What was the Mahdist uprising all about? It was a combination of the overthrow of oppressive Anglo-Egyptian colonial rule and a movement to establish a religiously-correct state. People supported the Mahdi and joined the Mahdists for many reasons: religious conviction, the personal charisma of the Mahdi, the belief that the Mahdists would reduce the oppression of the poor and bring about a more just society, fear of punishment for not joining the Mahdists, desire for loot, the chance to obtain more status and power, etc.

In the Mahdist state in the Sudan, the main successor of the Mahdi. Khalifa Abdallahi ibn Muhammad, ruled as a dictator maintaining power through violence and oppression when needed. Sharia law, smoking tobacco and drinking alcohol were banned and harshly punished. Private possession of firearms was banned to reduce the likelihood of uprisings. Otherwise, for most people, life went on as before.

The Khalifa attempted to extend the Mahdist state through conquest, to the north (Egypt), the east (Ethiopia) and the south, without success.

There are many parallels with other religious-revolutionary uprisings and the states they created such as the Taliban, the Islamic Revolution in Iran, and the Taiping.

The best source I know for details of everyday life in the Mahdist state is Joseph Ohrwalde, Ten years' captivity in the Mahdi's camp, 1882-1892: https://archive.org/details/tenyearscaptivit00ohrwuoft

For a broad view of the collision of the Mahdists with the rest of Africa and European colonialism, Thomas Pakenham, The Scramble for Africa.

For the Mahdi and the rise of the Mahdists, Kim Searcy, The Formation of the Sudanese Mahdist State, Brill 2011.

Another follow up question: Who killed Gordon?