A theocratic movement in Afghanistan with his origins in Islamic theology schools financed by Saudi Arabia that promoted a fundamentalist Islamic worldview and used its relative unity, by 2001, to become the dominant player emerging as a national government out of decades of civil war in Afghanistan that results when the Soviet Union withdrew from their occupation of the country. They did all the usual fundamentalist things (chopping off people's hands for stealing, attacking women for the slightest immodesty in their hyper-conservative view, destroying ancient Buddhist relics, etc, etc. and so forth).
A group called the Northern Alliance resisted them in a tiny part of the country. Opium production declined in their reign, but their real problem was that Osama bin Laden's al-Queda terrorist network based itself in their territory and when U.S. President George W. Bush, after the 9/11 attacks, decided that their cooperation with him in rooting out Osama bin Laden and his organization was insufficient, Bush invaded Afghanistan (allying itself with the Northern Alliance), and routed the Taliban in short order as part of his War on Terror.
Now the Taliban are a weakened guerilla force that operates in Afghanistan against the U.S. installed central government, which has elections on October 9, 2004, and the warlords who tolerate the existence of the central government but have not fully ceded power to it.
As of 2007 in adition to their gaining strengh in numbers and becoming bold enough to attack US bases the Talban it seems is now being armed by Chinese arms merchants.