We can say safely that the dominant people within the Magyar group was (well, modern Hungarians still are) speaking an Uralic language, usually attached to the ecosystem of the forests of northern and northwestern Russia (the best-known cognate of Hungarian nowadays is Finnish). However, it does not mean that their polity was ethnically united: confederations of steppe nomads are multi-ethnic (though we should not interpret this fact as unusual tolerance: rather, a successful ethnic and tribal group tended to subdue or attract less successful ones; these satellite forces retained their identities for a while, and then were absorbed by the elite culture, provided that it succeeded in maintaining the initial momentum of the group). Probably, there was some fluidity in border zones, and some Uralic groups had always been operating in the shadow of other Iranian, Turkic or Mongolian players; this time, we have no idea how, they managed to gain the upper hand. In fact, “steppe nomad” is probably as meaningful an identity as you can get. As for their early 9th century history, Regino of Prüm, a Carolingian chronicler, mentions that their flight to the West was a collateral damage of the conflict between Pechenegs (newcomers from central Asia) and Khazars (the great power of the Ponto-Caspian steppe); the Pecheneg confederation, fleeing Asia after a defeat, in turn triggered the migration of the Magyars, who may or may not have been tributaries of the Khazar qaghanate.