To add to the previous educators answer....

After Josep Broz Tito died in 1980, the new leader was Slobodan Milosevic.  An ethnic Serb, like Tito, he ruled Yugoslavia right before the USSR collapsed officially in 1991.  Many former satellite countries, free of the USSR, started to declare independence.  The six regions of Yugoslavia (Bosnia&Herzegovina, Croatia, Slovenia, Serbia, Montenegro, and Macedonia) started to break away. 

The biggest problems came when Bosnia&Herzegovina declared independence.  Unlike in Slovenia and Croatia, where most of the population were the same ethnicity, Bosnia was a hotbed of different ethnicities.  The largest three ethnicities in Bosnia in 1993 (at the time of independence) were the Bosnians (Muslims), Croats (Catholics), and Serbs (Christians).  Yugoslavia, a Serbian-run state, moved in to 'protect' the Serbian minority in Bosnia.  What occurred here was later coined "ethnic cleansing", or one ethnic/religious group getting rid of another ethnic/religious group using terror tactics (ranging from sexual assault, torture, and murder to imprisonment and forced deportation) to remove the latter ethnic/religious group from a country/region.  In this case, the Serbs attacked the Croats and Muslims in Bosnia, trying to rid Bosnia of the other ethnic groups.  Why?  To hopefully have a region that was fully Serbian and would likely stay part of the now smaller Yugoslavia.

For a time, there was little international response.  This changed after bombings at Sarajevo, the Bosnian capital, raised the alarm in the Western world.  NATO (North Atlantic Treaty Organization) stepped in, bombing Bosnia.  The Croats and Muslims were also launching a counter-attack on Milosevic's Serbian paramilitary and government forces, causing Milosevic to sign a peace treaty.

The end result: 200,000 Muslims and Croats ethnically cleansed as a result of Yugoslavia breaking apart.

What happened during the disintegration of Yugoslavia is that the country broke up into a number of smaller countries.  There are now five countries that have been created out of the territory that was once Yugoslavia.  The five countries are each dominated by a different ethnic group.  The disintegration of Yugoslavia and the creation of the new countries was accompanied by a great deal of ethnic violence.

The country of Yugoslavia was only created after WWI.  It was made up of a number of different regions with different ethnic groups.  After WWII, it became a communist country.  The authoritarian leadership, along with the personal prestige of the Yugoslav leader, Marshal Tito, kept the country together.  However, this did not mean that most Yugoslavs felt close ties with one another.

After Tito died in 1980, the Yugoslav state weakened.  This process was exacerbated by the fall of the Soviet Union and communism in the late ‘80s.  At that point, parts of Yugoslavia began to think of breaking away from the larger country.  As they did, there was a great deal of ethnic violence.  In areas that were home to multiple ethnic groups, conflict arose as to who would stay and who would be forced out.  There was massive “ethnic cleansing” of areas, a process in which minority ethnic groups were forced out of those areas.  There were atrocities committed by a variety of actors.  The conflict became so bad that the international community had to step in to try to prevent further bloodshed.

The disintegration of Yugoslavia, then, happened in a violent way.  Members of various ethnic groups fought each other as the country broke up into a number of smaller countries.