Kosovo becoming independent from the Serbs shouldn't seem particularly momentous -- it was mostly not Serbian, and they'd already had Slovenia, Croatia, Macedonia, Montenegro secede -- all of whom at least were Christians and spoke a Slavic language. The importance lies in the Battle of Kosovo -- a weird schadenfreude that brought the Serbs together in collective misery. They finally got it back when Serbia won independence from the Ottoman Empire in the late 19th century, but they never really got it back, because it had gone from being ethnically mixed to almost totally Albanian.
The impact of the Battle of Kosovo can be seen in the fact that it was the first major event to fall on Vidovdan, or St. Vitus' day. After that, beginning in the 20th century and coinciding with the strengthening of nationalism, half the events in Serbian-related history has occured on that day: the assassination of Franz Ferdinand; the treaty of Versailles; the founding of the Triune Kingdom of Serbs, Croates, and Slovenes (just rolls off your tongue!); the creation of the Cominform; Croatian independence; Milošević getting sent to the Hague; and finally Montenegro becoming independent. Too bad they couldn't have waited till June 28 and added Kosovo's independence to that list.