Andrej asked a couple of broad questions about the Ottoman Balkans, and there's no way I can do that whole topic justice in a blog post. What I'm going to do instead is focus on one of his questions, why some Balkan peoples converted to Islam while the vast majority did not. And to make things more specific, I'm going to focus on the Bosniak people and leave the Albanians aside. Andrej (or anybody else), if there are more aspects of the Ottoman Balkan picture that you'd like me to write about, please feel free to drop another question into the comments of the appropriate post.
Bosnia and Herzegovina is today only slightly majority Muslim, but that's due to the large populations of mostly Catholic Croats and mostly Orthodox Serbs living there. The vast majority of Bosniaks themselves are Muslim, though I think it's important to point out that this is in some ways as much a cultural marker as it is a religious one. The Bosnian War, as you might expect, caused some intensification of religious views among all three of the country's major ethnic communities, but Bosniak Islam, though almost all Sunni, is pretty loosely organized compared to, say, rigid Gulf Wahhabism. Sufism is a major component of Bosniak Islam, for example.
When we consider why the Bosniaks wound up by and large converting while other Slavic peoples did not, I think the first thing we need to say is that there's very little to no evidence of coercion. And, really, that makes sense. Why, after all, would the Ottomans have singled this one community out for coerced conversion to Islam but left Serbs, Croats, Macedonians, Greeks, Bulgarians, etc., alone to maintain their Christianity? Nobody has ever, to my knowledge, produced any evidence that the Ottomans one day said "these people, living in this one specific area, must be converted, but we'll leave everybody else alone."
Moreover, the pre-17th century Ottoman system actually depended on maintaining large Christian populations in the Balkans. Christian families paid extra taxes, don't you know, and--more importantly--their male children were subject to the devşirme, the conscription program that filled the ranks of both the Ottoman bureaucracy and the Janissaries. Conscripts were forcibly converted, but if the Christians of the Ottoman Empire had all converted themselves then this critical source of manpower would have disappeared overnight, since Muslims were forbidden from enslaving other Muslims. Indeed, the Ottomans organized their empire around allowing these communities to keep their own religion and legal codes--though obviously Ottoman law superseded in the case of a conflict--in what was eventually formalized as the millet system. This wound up coming back to bite them in the imperial ass, as the millets later became vectors for the nationalist movements that eventually tore the Empire apart.
(In parts of Albania, coercion did play a role, but only starting in the 18th century or so, when the Ottomans began to regard Orthodox Albanians as nothing but a source of perpetual rebellion and excuse for Russian interference.)
So why did the Bosniaks convert? Well, the answer is already embedded in that religious breakdown of Bosnia and Herzegovina a couple of paragraphs ago. The country's two largest ethno-religious minorities are the Catholic Croats and the Orthodox Serbs, who had deep pre-Ottoman roots in those very well established churches. The Bosniaks, on the other hand...didn't. In fact, Bosnia was right on the border between the two churches, and efforts to proselytize there were tricky, because the region was geographically difficult to navigate and lacked major cities where preachers could pitch their message to large groups of unconverted people (Sarajevo didn't really start to become a large urban area until after the Ottoman conquest).
As a result, the pre-Ottoman Banate of Bosnia, nominally part of Hungary but for all intents and purposes independent, became a safe haven for Bogomilism. This was a gnostic heresy founded in the Bulgarian Empire in the 10th century by a priest named--wait for it--Bogomil. We know pretty much nothing about Bogomil, but his movement spread to pockets all over Europe (the Cathars, for example, the targets of the Albigensian Crusade, were Bogomilists). His followers believed, as gnostics tend to do, in dualism, meaning the total separation of the good/spiritual world and the evil/physical world, which is entirely heretical within Christianity. After several unsuccessful Hungarian-led efforts to Catholicize the region's Bogomilists, also known as Patarenes, the Church actually called a Crusade (1235-1241) that had about as much success as most other Crusades--which is to say none, more or less.
Bogomilism may not have been the only heterodox religious movement that found a home in Bosnia--there's at least one source that says the region was home to a population of Manicheans (!), which is a Zoroastrian (!!) offshoot that goes all the way back to 3rd century Persia.
All this Bogomilism talk is just to say that the Bosniak introduction to Christianity, of both the eastern and western varieties, was not very positive. At some point in the 12th-13th centuries the Bosnian Church was formed. This was a Christian church, which is sometimes identified as Bogomilist but probably wasn't, but that nevertheless remained firmly independent of both the Catholic and Orthodox Churches. It's not clear how large the Bosnian Church was, just as it's not clear how many Bogomilists were really roaming around Bosnia during this period, and not much is known about its actual beliefs/practices other than that its liturgy was conducted in Slavic and its writings seem pretty consistent with, say, 13th century Catholicism (that's why the assertion that it was Bogomilist doesn't really hold water). We also don't know when the Bosnian Church disappeared, whether it was before or after the Ottoman arrival.
Anyway, you're waiting for me to get to a point, and here it is: when the Ottomans rolled through the Balkans in the middle of the 15th century, they found established Orthodox peoples like the Serbs, established Catholic peoples like the Croats...and then there were the Bosniaks, who really didn't have an established connection to Christianity. There were no deep cultural or familial ties keeping Bosniaks within the Christian world. And so now we can talk about the other factor at play here, which is that, as you might imagine, there were a lot of reasons why it was good to be a Muslim in the Ottoman Empire. You could move around more freely, advance farther in society. You avoided the extra taxes that Christians paid, and--crucially--you didn't have to bear having your sons taken away and drafted into the Ottoman regime.
In some sense, the real question isn't why the Bosniaks converted, but why other Slavic peoples didn't. And as we've seen, this largely had to do with the cultural link between those other peoples and some version of Christianity--a link the Bosniaks never really formed. Without that link, it must have been easier to justify adopting Islam and the benefits that came with it, particularly when conversion, under the Ottoman Empire, wasn't particularly onerous. Just as they weren't in the business of coerced conversion (at least, not yet), the Ottomans also weren't in the business of forcing their Muslim subjects to adhere to any rigid single kind of Islam. So the folk traditions, which--in the absence of a heavy Catholic or Orthodox presence--were the real Bosniak religion, were smoothly adapted to an Islamic context (you can see this folk religion manifested in the popularly of Sufism).
The Bosniak people didn't convert en masse. This was a gradual change that began after the region became Ottoman territory in the mid-15th century. But by the 17th century the community was predominantly Muslim. In fact, 17th century Bosnia was probably far more Islamic than modern Bosnia and Herzegovina--as the territory's boundaries and peoples have changed, and the proportion of Croats and Serbs living there has increased, so Muslims have decreased as a percentage of the total population.
I've added a map that shows Ottoman expansion from the mid 15th century through the mid 16th century in case that helps you visualize things.