The Pashto word, Taliban means "students," and derives from the Arabic word for student, talib (the plural, in Arabic, is tullab). The Taliban rose from the ranks of religious seminary students, thus their name.
The Taliban began to organize into an armed political organization in the early 1990s., and existed in fully fledged form by 1994.
Backing & Affiliation:
The Taliban arose from among the Afghan refugees who flooded Pakistan during the Afghan-Soviet war, which ended with Soviet withdrawal in 1989. Pakistan nurtured, and helped arm, the nascent militia. The Taliban also received support from Saudi Arabia and indirectly from the United States, which funded Pakistan.
The Taliban sought to wrest control of Afghanistan from the several mujahideen factions who controlled it in the wake of the Soviet withdrawal. During their reign from 1996 to 2001, the Taliban sought to impose severe authoritarian rule on Afghanistan, and to gain legitimate acceptance for it by claiming it as Islamic.Under Taliban rule, basic human rights were egregiously restricted; the withdrawal of basic rights from women: to freedom of movement, medical care and education was infamous (though generally not acted on in the world community).
The Taliban & Osama bin Laden:
Osama bin Laden was an ambitious and pious financier of the mujahideen when he first went to Pakistan in 1980. From Pakistan he recruited Arab Muslims to fight the Afghan cause (Afghans are of several ethnicities, but they are not Arab and don't speak Arabic, but Pashto, Dari and Farsi/Persian). After being kicked out of Sudan in 1980, Osama bin Laden resettled in Taliban run Afghanistan, which provided him and his training camps safe haven.
The U.S. & the Taliban:
After the 9/11 attacks, the United States demanded that the Taliban turn over bin Laden to their custody. After several rounds of the negotiation, which included the Taliban's suggestion that bin Laden be tried in Afghanistan, the U.S. commenced bombing of Afghanistan on October 7, 2001. The Taliban immediately endured significant losses, and by December 2001, an interim goverment headed by Hamid Karzai is in its initial stages.
Despite claims by the Bush Administration that the Taliban had been decisively defeated by the American attacks, this was not really the case, although the Taliban government was taken down. Over the course of 2006, it became clear that a Taliban insurgency of significant strength was shaping up. The Taliban have also begun to use suicide bombing as a tactic against the NATO and ISAF forces.