The Bosnian War was part of a larger series of wars surrounding the breakup of Yugoslavia, which included relatively large wars in Croatia and Kosovo, and smaller ones in Slovenia and Macedonia. The war in Bosnia actually didn't start until almost a year after the outbreak of war in Croatia, so it's necessary to look at why Yugoslavia began to dissolve in the first place.
The key player in Serbia during this time was a guy called Slobodan Milosevic. He came to power in the mid '80s as the President of Serbia, which was the largest republic within Yugoslavia and home to the country's capital, Belgrade. One of his goals was to elevate the status of Serbia within Yugoslavia, and he did this through the "anti-bureaucratic revolution." Basically, Milosevic staged protests throughout Serbia to kick out local government officials and replace them with his own friends. This way, Milosevic hoped to gain control of a large voting block in the Yugoslav presidency, which since the death of Marshal Tito had been comprised of representatives from each of the 6 Yugoslav republics and 2 autonomous provinces (Kosovo and Vojvodina).
Well, the other republics weren't too happy about this new plan, especially Slovenia and Croatia. Shit went down in early 1990, when Slovenia and Croatia walked out of the 14th Congress of the League of Communists, and Slovenia later held a referendum for independence. After a brief military engagement, Milosevic let Slovenia go, since there weren't many Serbs there that would support him. When Croatia separated, however, the Yugoslav army intervened to "protect" Serbs, which included campaigns of ethnic cleansing to remove Croats from places like Vukovar.
The way Milosevic rallied people was by inciting ethnic nationalism and creating a campaign based on fear of other ethnicities. Nowhere was this more damaging than Bosnia, which didn't have a clear majority population like the other republics. In 1990, the population was about 40% Bosniak (Muslim) 30% Serb, 20% Croat, and 10% other iirc. Plus, these people were all living together with one another, sharing communities, schools, and everything else. There was a high rate of mixed-marriages, and there wasn't a clear boundary between the territory of one ethnicity and another. It was all mixed up. You can look up a map of Bosnian ethnicities in before and after the war and see the effect that the war had.
So as ethnic propaganda began to flood Bosnian television and radio, people began to get scared. They became convinced that if other ethnicities were in power, their kids wouldn't be able to go to school, or they would be fired from their job, or things like that. A common misconception is that it was just Serb nationalism that was inflamed, and that Serbs were the sole aggressors in the war. Although Serbs were the best equipped side and did pursue an aggressive campaign of ethnic cleansing, Croats and Bosniaks also separated into ethnic blocks and removed other groups from the territory they held during the war. It got really messy all around.
Let me share a story I heard when I was in Sarajevo a few months ago. My friends and I went on a tour around the city, and our tour guide was a cool young guy who was born in Sarajevo. He told us his father was a Muslim and his mother was a Serb, and when ethnic propaganda began to enter Bosnia, they were worried about what would happen to their mixed-race child. He said that just before the war, his mother's brother was approached by Serb police and given an AK-47, because they told him that he would need it. When war finally broke out in 1992, our guide and his father fled to Muslim territory, and he couldn't tell anyone that his mother was a Serb, he just said she was dead. It's that kind of stuff that made Bosnia the messiest war, and it really is a tragedy.
When I try to explain how fucked up it all was to my family back here in America, I usually ask them what would happen if all the people in Los Angeles who identified as Mexican rose up with weapons and demanded their own country? Imagine how ridiculous that would be, if your Mexican neighbor who you've lived next to for 30 years just decided to kick you out of your house because you lived on "Mexican territory." It's obviously not a direct parallel, but it was that kind of messy in Bosnia, and it completely tore the country apart.
Sorry if this was a little scatterbrained, I'm on my phone and I just woke up. If you want a good overview of the whole thing, I'd highly recommend the BBC's Death of Yugoslavia documentary. It's pretty comprehensive and they interview all the major players, which is really fascinating. There are many more facets to this issue that I know I didn't cover, and maybe I'll add more after I eat breakfast, but I hope I hope this helped somewhat. If you have any questions feel free to ask.