Oscillator sync makes one oscillator, the follower, restart its cycle each time another oscillator, the leader, completes a cycle. The follower is forced to the pitch of the leader, but its waveform is cut off and reset, which adds strong harmonics.
Sweeping the follower’s pitch while it is synced creates the classic tearing lead sound. Hard sync restarts the waveform abruptly, and soft sync does it more gently or only partly.