While Buddhism undermined the concept of a permanent soul or self, it still had the problem of explaining karma as a kind of moral retribution on the individual in future lives despite the lack of a soul.
The explanation developed for this question is that karma exists by virtue of habitual mental energies (samskaras) that are impressed on consciousness (vijnana). In this way, vijnana endures for the duration of one’s life and is then reincarnated in the next life.