The roots of the Kosovo War began with World War II. During this time, Yugoslavia, which Kosovo was part of, was ruled by General Tito. Tito allowed Albanian refuges to move into the region during World War II which agitated the local Serbian population. Many of them began to leave when the economy tanked, and after Tito died the population was roughly 50% Albanian and 50% Serbian.
The Albanian population of Kosovo began seeking independence, sometimes violently, which led to Serbian police oppression. The Albanians began seeking foreign support for their movement in the hopes of gaining money for weapons to support their fight.
When Slobodan Milosevic came to power in Yugoslavia, he cracked down on Kosovo, using military power and horrific war crimes to try and pacify the population. The people of Kosovo fought back and soon the situation was drawing international attention. This is what led to the eventual involvement of NATO.