There are a few answers to your question here:

1. Access to money and power

It might seem obvious, but Muslims had access to a privileged status in the Ottoman Empire. If you had political ambitions, conversion to Islam was necessary.

Also, Islamic law mandates the charging of a tax on non-Muslims called the "jizya". You might know people today who do anything to lower their taxes, so this was another motivator.

2. To keep your kids around

Balkan Christians were subject to another tax, the devşirme or "blood tax". Boys between 8 to 20 years old would be taken forcibly from their homes, taken to Constantinople, converted to Islam and trained for roles in civil service and the janissaries (professional soldiers).

Some of these slaves rose to high positions, even that of Grand Vizier, 2nd only to the Sultan (I use the word "slave" because they were taken forcibly, but also because everyone in the Ottoman Empire was technically a slave of the Sultan).

Due to the possibility of success as one of these slaves, there were families who offered their boys up willingly. But while I am not aware of any primary source indicating conversion to Islam to avoid the devşirme, this would not seem to be too far of a stretch.

3. Dissatisfaction with both the Catholic and Orthodox Church apparatuses

At the time in the Balkans, you had two choices of religion: Catholicism and Orthodoxy, both Christian. Paganism was strongly discouraged, if not outright persecuted. BUT believing in Jesus did not always keep you safe from persecution.

A "heretical" sect had arisen in the Balkans, known as "Bogomilism". It began in Bulgaria and seems to have taken hold especially in modern Bosnia and Herzegovina. Not only did they not adhere to traditional Catholic or Orthodox doctrine, they also spurned church and political hierarchies.

This, of course, was a no-no for the various church fathers, kings and tsars of the area, so the Bogomils were persecuted as heretics by both Churches and political elites.

One theory why Islam seems to have taken particular hold in Bosnia and Herzegovina is due to their history with Bogomilism and their recent memory (at the time of Ottoman conquest) of poor treatment by both sides of the Christian world.

Side note: there is a possibility that the slang word "bugger", meaning "anal sex", comes from the word "Bulgar". The idea is that this is a relic of anti-Bogomil propaganda and smear campaigns which has persisted over the ages.

I unfortunately cannot weigh in on why Islam took such a hold in Albania, which is somewhat ironic given their history of fierce resistance towards the Ottomans (look up their national hero, Skanderbeg). However, Islam in Kosovo can largely be explained by the massive Kosovar Albanian population, which likely immigrated from Albania.

There are other important demographic considerations, mainly that the map of religions in 2022 does not reflect the reality over the centuries.

With the original Ottoman invasions and during periodic repression of Christians in later years, huge waves of Balkan Christians migrated North to majority Christian nations. Conversely, with the Balkan Wars in the 1800s, often revolts against the Ottoman Empire which resulted in nation-states led by Christians, Balkan Muslims relocated to the remaining Empire, willingly or otherwise.

And of course, let's not forget the ethnic cleansing and genocide of WWII and the wars of the 1990s, which also affected the religious makeup of the region. Serbia had a significant Muslim community, as did coastal Romania, which still exist, though greatly diminished.

In short, today's map can reflect more basic trends like war and population transfer as well.

/u/UrbisPreturbis has previously answered a similar question

/u/Chamboz has previously answered Why is Islam more common in the countries near the Adriatic Sea such as Albania, Kosovo, Bosnia-Herzegovina, etc and less common in the countries closer to Turkey like Bulgaria, Greece and Serbia? with follow-up questions too.