To understand the Afghanistan conflict you need to know the history of Afghanistan. Up until 1973, Afghanistan was ruled by a monarch the last one, Muhammad Zahir Shah being ousted in a coup led by his cousin Daoud Khan. To spare you all the complicated bits (which would take up an entire book) Daoud Khan's coup set off an era of chaos in Afghanistan. Eventually the communists would take over in the late 1970s and the 1980s and then civil war in the 1990s.
Afghanistan is a country with 5 major ethnic groups: the largest two are the Pashtuns and Tajiks. The Pashtuns are generally in the south and east (along the border with Pakistan) and the Tajiks are in the north. The smaller sectarian groups are the Uzbeks and Turkmen, and the Hazeras (who are Shiite instead of Sunni) most of which live in the north as well. Additionally, the Pashtuns are divided between Pakistan and Afghanistan as the boundary between the two countries (called the Durand line) was drawn by the British in an effort to divide the Pashtun people to make them easy to pacify and less of a threat to then British controlled India, Movement back and forth between the two countries is pretty common place and easy.
It is in this context that one has to understand the Taliban and the current conflict. The Taliban (Arabic for "students") traces its lineage back to schools in British India run by conservative Muslims from the Deobandi school of Islamic thought (a close relative of Saudi Wahabism). However, because the Taliban is a movement from British India, its members are almost all from the Pashtun ethnic group and many of the early leaders of the Taliban were from the Duranni tribe (the same tribe as the last king of Afghanistan). In the mid 1990s when the Taliban first began to rise to power in Afghanistan these facts alarmed many in Afghanistan, some thought they represented a Pashtun nationalist movement and others thought they aimed to bring back the monarchy. Those alarmed formed an alliance to fight the Taliban which in the west was called the Northern Alliance, and they chose former anti-Soviet leader Ahmed Shah Massoud as their leader.
How does this apply today? The U.S. took out the Taliban and a new government has taken power. However, elements of the Taliban still exist and many Pashtuns in Afghanistan still support the Taliban (they worry that if the Taliban are gotten rid of no one will stand up for Pashtun interests) while others do not want the Taliban (some want democracy, others want power for themselves instead). The major issue for the U.S. and the Afghan government is whether to compromise with whatever is left of the Taliban or to continue to fight them. If you compromise, you risk returning Afghanistan back to its bloody past, but if you don't, you risk alienating the Pashtuns thus making the south and east of the country ungovernable. Truly a tricky situation.
Believe it or not this is a really short answer, I skipped a lot of things.
A ton of reading.