We really don't know. There are multiple theories, but there is no conclusive evidence for any of them.

1. The theory which seems to be the current consensus among Hungarian scholars, is that the Carpathian basin was sparsely populated at the end of the IXth century, and the Hungarian tribes moving in were more numerous than previous conquerors, so they could avoid being assimilated like it happened to Bolghars for example.

2. The least widely held theory is that the Hungarian conquerors became the aristocracy of the Carpathian basin and the language of the conquerors substituted that of the conquered. This theory is mostly rejected precisely because there are very few examples of happening this throughout history.

3. László Gyula, a prominent archeologist of the last century suggests that there is a surprising continuity in the Carpathian basin pre and post the Hungarian conquest. According to his findings the settlements of half-settled natives continued to exist in numbers, and the biggest change is that signs appear of some less sedentary people who moved around in a more nomadic fashion for. László argues that Árpád and his warriors were indeed a minority, and have been assimilated into a finno-ugric population which has been living in the Carpathian Basin since at least the VIth century - they would be none others than the Pannonian Avars. He assumes (because of archeological similarities) that the conquering "Hungarians" at the end of IXth century were actually a Turkic people.

This last theory is interesting, but it isn't well-regarded today, and what's more, it doesn't really solve the question why Hungarian became the language spoken in the Carpathian Basin. All it does is just pushing back the time of the language-change three hundred years.