The Taliban started as a Mujahideen faction working to remove the Soviet Union and its control from Afghanistan, but didn't become a larger, more powerful group until the 1990s. The Soviets were removed from power in the country, but it quickly turned to civil war between the Mujahideen factions and others once they were gone.
The Taliban controlled a large portion of Afghanistan by 1994 and continued to control the country until 2001. Following the attack on the United States by Al-Qaeda terrorists, the Taliban was routed from power. The Taliban had become a breeding ground for the terrorist to recruit and train new members before sending them out to attack targets.