The Taliban—from the Arabic word for student, “taleb”—are fundamentalist Sunni Muslims, mostly from Afghanistan’s Pashtun tribes. The Taliban dominates large swaths of Afghanistan and a large part of Pakistan’s Federally Administered Tribal Areas.
The Taliban seek to establish a puritanical caliphate that neither recognizes nor tolerates forms of Islam divergent from their own. They scorn democracy or any secular or pluralistic political process as an offense against Islam. The Taliban’s Islam, however, a close kin of Saudi Arabian Wahhabism, is far more perversion than interpretation. The Taliban’s version of Islamic law, or Sharia, is historically inaccurate, contradictory, self-serving and fundamentally deviant from prevailing interpretations of Islamic law and practice.

There was no such thing as a Taliban until the Afghanistan’s civil war in the wake of Soviet troops’ withdrawal in 1989, after a decade-long occupation. But by the time their last troops withdrew in February 1989, they’d left a nation in social and economic shards, 1.5 million dead, millions of refugees and orphans in Iran and Pakistan, and gaping political vacuum that warlords attempted to fill. Afghan mujahideen warlords replaced their war with the Soviets with a civil war.
Thousands of Afghan orphans grew up never knowing Afghanistan or their parents, especially their mothers. They were schooled in Pakistan’s madrassas, religious schools which, in this case, were encouraged and financed by Pakistani and Saudi authorities to develop militantly inclined Islamists. Pakistan nurtured that corps of militants as proxy fighters in Pakistan’s ongoing conflict with over Muslim-dominated (and disputed) Kashmir. But Pakistan consciously intended to use the madrassas’ militants as leverage in its attempt to control Afghanistan as well.

As Jeri Laber of Human Rights Watch wrote in the New York Review of Books of the origins of the Taliban in refugee camps (recalling an article he’d written in 1986),

Hundreds of thousands of youths, who knew nothing of life but the bombings that destroyed their homes and drove them to seek refuge over the border, were being raised to hate and to fight, “in the spirit of Jihad,” a “holy war” that would restore Afghanistan to its people. “New kinds of Afghans are being born in the struggle,” I reported. “Caught in the midst of a grownups’ war, the young Afghans are under intense political pressure from one side or another, almost from birth." [...] The children that I interviewed and wrote about in 1986 are now young adults. Many are now with the Taliban.

As civil war was ravaging Afghanistan, Afghans were desperate for a stabilizing counter-force that would put an end to the violence.
The Taliban’s most original aims were, as Ahmed Rashid, the Pakistani journalist and author of Taliban (2000), wrote, to “restore peace, disarm the population, enforce Sharia law and defend the integrity and Islamic character of Afghanistan.

As most of them were part-time or full-time students at madrassas, the name they chose for themselves was natural. A talib is an Islamic student, one who seeks knowledge compared to the mullah who is one who gives knowledge. By choosing such a name the Taliban (plural of Talib) distanced themselves from the party politics of the mujahideen and signaled that they were a movement for cleansing society rather than a party trying to grab power.”

For their leader in Afghanistan, the Taliban turned to Mohammed Omar, an itinerant preacher likely born in 1959 in Nodeh village near Kandahar, in southeastern Afghanistan. He had neither tribe nor religious pedigree. He had fought the Soviets and been wounded four times, including once in the eye. His reputation was that of a pious ascetic.

Omar's reputation grew when he ordered a group of Taliban militants to arrest a warlord who had captured two teenage girls and raped them. The 30 Talibs, with just 16 rifles between them—or so goes the story, one of many near-mythical accounts that have grown around Omar’s history—attacked the commander’s based, freed the girls, and hanged the commander by their favorite means: from the barrel of a tank, in full view, as an example of Taliban justice.

The Taliban’s reputation grew through similar feats.